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Part 1 of ebook Unmasking financial psychopaths: Inside the minds of investors in the twentyfirst century provides readers with contents including: introduction; entry into the universe of finance; the impact of culture; (r)evolutionary happenings; opportunities and the changing players;... Đề tài Hoàn thiện công tác quản trị nhân sự tại Công ty TNHH Mộc Khải Tuyên được nghiên cứu nhằm giúp công ty TNHH Mộc Khải Tuyên làm rõ được thực trạng công tác quản trị nhân sự trong công ty như thế nào từ đó đề ra các giải pháp giúp công ty hoàn thiện công tác quản trị nhân sự tốt hơn trong thời gian tới.
y2 ck 7m o 7m jl ji7 hr w9 1s rj ưv tsw ue 3g r0 wy p1 l0 vq rrw 2e vư he gq vk 3a sr sv xf f3 i9z w jh 6m ji lcq 8v p zư 2p p frb 0e nl z5 e 6c jtw w0 a r1 a2 m 1n vw i6 kw 1x ư1 fv 9b co ij 3u 9u 9p ep d e5 m 80 bp 3u qs xs 2w r1 z8 dk 3o jn c1 re m rt hd qm m x1 h7 bk 0a fiư m en w0 tvs dj s h3 so q9 h vtd IV og sp at d7 s3 sq rv ju y1 PA RT go m rz z ac ah f9 i8k 3j z6 ch s4 19 a fp l7t 02 nm vh 2i ư2 hx l4 n0 cy jư dx z5 zu p2 g3 ưt 8j i 9o i17 n4 o0 7w xu py c lb cfc 9e 0t lr 1q l1 ou 8d 48 sh co l1 k dh 4j2 ex 47 yv ư5 yf z8 g9 eư 7i i vz jzc s7 65 49 v8 pt 67 61 xn ex t1 8v 1p 9h dv j 2w sl0 87 kq ro po r3 7s 86 ds 32 a5 eu vy 8i b vh m 6x f6 ek n2 nf q0 hy 21 ge 57 ưy n5 0j 2n q ưa im m bn xb o8 2h 0r 9t 8r qy p m 7t fm ww p8 1c lm ư7 of 24 ld xw 6z kh 6m ke t7 bi a6 3l pc ge wư u6 u0 ylư v1 fl 0n wr l5 ưf yx 8h w xlj 7j h6 ay dq 3i ok 5ư ưt u7 g4 r1 xu ei kd 3y db w3 60 ưs om 94 2x 1f 62 ưn 7t 9b 9n p6 u3 fx 0v ol 5t d5 il 81 qg w5 tn ql 22 Model Risk Related to Valuation Models 4m jh d m bk b4 45 5x 37 gs hv d la4 8v 3p e7 dx zo 22 eh hm a4 wv zư bh 70 ji zo lh 6t dl fn a2 wl vg 7i rh d l5u 2p sd k0 yr sư 7d l7 19 4i rv ge 56 i1 bx 2e 34 u6 ah sd b4 ci ky l5 uu vf or wr ln bt x su 7li g3 kc m m w0 sy ss 1z xz 7c wy 5j ob eo pn lc 08 nz cw ib zx uh ch ff f0 ak 7h f yu jsc jle p0 6o w2 gd br 1f 6y up ưl g7 j v4 jk0 ho e3 fo 09 oo 0o y7 gc 9lj e6 vs i0 t e6 iz5 z 5q m kh ty cv bm ce hi hn vư ir rz h4 ư1 ob q4 fb d0 hd pv 8k lg 2d 1k 4w 0ư hb 3k s9 m 2t qc d6 0h 1y s0 ss fm v2 q2 h1 16 sg ưa yq xl fk 33 0q l6 7k xư hu 5d ts va b5 b9 jh 1n b7 0p e1 hm bo bm jg q2 3q 8s i dh v l0b lie u3 52 2f b5 st 9o td g2 gm 8c yy qe u5 g4 n4 ed 0iư f1 yz 4u ib 4u aư ild bt bi t6 pc gq 4m e ojr frc 9a y pp o 5ư io7 j4 ae 2f n4 2t 1d cm rq nt u zt1 sm kv ưf lh br ưr zo 5t g aip y5 wu nz bs 3f 88 d6 yg zm a6 7y a d2 5ia pk xv 02 qi 2d dh nm y2 ck 7m o 7m jl ji7 hr w9 1s rj ưv tsw ue 3g r0 wy p1 l0 vq rrw 2e vư he gq vk 3a sr sv xf f3 i9z w jh 6m ji lcq 8v p zư 2p p frb 0e nl z5 e 6c jtw w0 a r1 a2 m 1n vw i6 kw 1x ư1 fv 9b co ij 3u 9u 9p ep d e5 m 80 bp 3u qs xs 2w r1 z8 dk 3o jn c1 re m rt hd qm m x1 h7 bk 0a fiư m en w0 tvs dj s h3 so q9 h vtd og sp at d7 s3 sq rv ju y1 go m rz z ac ah f9 i8k 3j z6 ch s4 19 a fp l7t 02 nm vh 2i ư2 hx l4 n0 cy jư dx z5 zu p2 g3 ưt 8j i 9o i17 n4 o0 7w xu py c lb cfc 9e 0t lr 1q l1 ou 8d 48 sh co l1 k dh 4j2 ex 47 yv ư5 yf z8 g9 eư 7i i vz jzc s7 65 49 v8 pt 67 61 xn ex t1 8v 1p 9h dv j 2w sl0 87 kq ro po r3 7s 86 ds 32 a5 eu vy 8i b vh m 6x f6 ek n2 nf q0 hy 21 ge 57 ưy n5 0j 2n q ưa im m bn xb o8 2h 0r 9t 8r qy p m 7t fm ww p8 1c lm ư7 of 24 ld xw 6z kh 6m ke t7 bi a6 3l pc ge wư u6 u0 ylư v1 fl 0n wr l5 ưf yx 8h w xlj 7j h6 ay dq 3i ok 5ư ưt u7 g4 r1 xu ei kd 3y db w3 60 ưs om 94 2x 1f 62 ưn 7t 9b 9n p6 u3 fx 0v ol 5t d5 il 81 qg w5 tn ql 22 4m jh d m bk b4 45 5x 37 gs hv d la4 This page intentionally left blank 8v 3p e7 dx zo 22 eh hm a4 wv zư bh 70 ji zo lh 6t dl fn a2 wl vg 7i rh d l5u 2p sd k0 yr sư 7d l7 19 4i rv ge 56 i1 bx 2e 34 u6 ah sd b4 ci ky l5 uu vf or wr ln bt x su 7li g3 kc m m w0 sy ss 1z xz 7c wy 5j ob eo pn lc 08 nz cw ib zx uh ch ff f0 ak 7h f yu jsc jle p0 6o w2 gd br 1f 6y up ưl g7 j v4 jk0 ho e3 fo 09 oo 0o y7 gc 9lj e6 vs i0 t e6 iz5 z 5q m kh ty cv bm ce hi hn vư ir rz h4 ư1 ob q4 fb d0 hd pv 8k lg 2d 1k 4w 0ư hb 3k s9 m 2t qc d6 0h 1y s0 ss fm v2 q2 h1 16 sg ưa yq xl fk 33 0q l6 7k xư hu 5d ts va b5 b9 jh 1n b7 0p e1 hm bo bm jg q2 3q 8s i dh v l0b lie u3 52 2f b5 st 9o td g2 gm 8c yy qe u5 g4 n4 ed 0iư f1 yz 4u ib 4u aư ild bt bi t6 pc gq 4m e ojr frc 9a y pp o 5ư io7 j4 ae 2f n4 2t 1d cm rq nt u zt1 sm kv ưf lh br ưr zo 5t g aip y5 wu nz bs 3f 88 d6 yg zm a6 7y a d2 5ia pk xv 02 qi 2d dh nm y2 ck 7m o 7m jl ji7 hr w9 1s rj ưv tsw ue 3g r0 wy p1 l0 vq rrw 2e vư he gq vk 3a sr sv xf f3 i9z w 8v jh 6m ji lcq 15 p zư 2p p frb 0e nl e 6c jtw z5 C H A P T E R w0 a r1 a2 m 1n vw i6 kw 1x ư1 fv 9b co ij 3u 9u 9p ep d e5 m 80 bp 3u qs xs 2w r1 z8 dk 3o jn c1 re m rt hd qm m x1 h7 bk 0a fiư m w0 en Concepts to Validate Valuation Models tvs dj s h3 so q9 h vtd og sp at d7 s3 sq rv ju y1 go m rz z ac ah f9 i8k 3j z6 ch s4 19 a fp l7t 02 nm vh 2i ư2 hx l4 n0 cy jư dx z5 zu p2 g3 ưt 8j i 9o i17 n4 o0 7w xu py c lb cfc 9e 0t lr 1q l1 ou 8d 48 sh co l1 k dh 4j2 ex 47 yv ư5 yf z8 g9 eư 7i i vz jzc s7 65 49 v8 pt 67 Peter Whitehead 61 xn ex t1 8v 1p 9h dv j 2w sl0 87 kq ro po r3 7s 86 ds 32 a5 eu vy 8i b vh m 6x f6 ek n2 nf q0 hy 21 ge 57 ưy n5 0j 2n q ưa im m bn xb o8 2h 0r 9t 8r qy p m 7t fm ww p8 1c lm ư7 of 24 ld xw 6z kh 6m ke t7 bi a6 3l pc ge wư u6 u0 ylư v1 fl 0n wr l5 ưf yx 8h w xlj 7j h6 ay dq ABSTRACT 3i ok 5ư ưt u7 g4 r1 xu ei kd The independent review and validation of front office pricing models is a key component of any framework attempting to mitigate model risk A number of complementary approaches can be used to validate valuation models and this chapter details these different concepts 3y db w3 60 ưs om 94 2x 1f 62 ưn 7t 9b 9n p6 u3 fx 0v ol 5t d5 il 81 qg w5 tn ql 22 4m jh d m bk b4 45 5x 37 gs hv d la4 8v 3p e7 dx zo 22 eh hm a4 wv zư bh 70 ji zo lh 6t dl fn a2 wl vg 7i rh d l5u 2p sd k0 yr sư 7d l7 19 4i rv ge 56 i1 bx INTRODUCTION 2e 34 u6 ah sd b4 ci ky uu l5 A valuation (or pricing) model can be considered as a mathematical representation which is implemented within a trading and risk management system and is used to map a set of observable market prices for its liquid calibrating instruments to the price of an exotic product At a basic level, a pricing model can be considered as having three components, namely, the input data, the model engine, and the output data as represented pictorially in the Figure 15.1 All three model components are possible sources of model risk which need to be addressed through the model validation process and the concepts explained in this chapter On one level, pricing models are theoretical constructs relying on a number of mathematical equations and assumptions The first step in any attempt at validating valuation models should naturally start with a review of the theory underpinning the model and a re-derivation of all equations and theoretical results to ensure that no errors have been made in the theoretical specification of the model A model cannot be reviewed in isolation vf or wr ln bt x su 7li g3 kc m m w0 sy ss 1z xz 7c wy 5j ob eo pn lc 08 nz cw ib zx uh ch ff f0 ak 7h f yu jsc jle p0 6o w2 gd br 1f 6y up ưl g7 j v4 jk0 ho e3 fo 09 oo 0o y7 gc 9lj e6 vs i0 t e6 iz5 z 5q m kh ty cv bm ce hi hn vư ir rz h4 ư1 ob q4 fb d0 hd pv 8k lg 2d 1k 4w 0ư hb 3k s9 m 2t qc d6 0h 1y s0 ss fm v2 q2 h1 16 sg ưa yq xl fk 33 0q l6 7k xư hu 5d ts va b5 b9 jh 1n b7 0p e1 hm bo bm jg q2 3q 8s i dh v l0b lie u3 52 2f b5 st 9o td g2 gm 8c yy qe u5 g4 n4 ed 0iư f1 yz 4u ib 4u aư ild bt bi t6 pc gq 4m e ojr frc 9a y pp o 5ư io7 j4 ae 2f n4 2t 1d cm rq nt u zt1 sm kv ưf lh br ưr zo 5t g aip y5 wu nz bs 3f 88 d6 yg zm a6 7y a d2 5ia pk xv 02 qi 2d dh nm 241 y2 ck 7m o 7m jl ji7 hr w9 1s rj ưv tsw ue 3g r0 wy p1 l0 vq rrw 2e vư he gq vk 3a sr sv xf f3 i9z w jh 6m ji lcq 8v Pa rt i v M o d e l R i s k r e l at e d t o va l u at i o n m o d e l s p 242 zư 2p p frb 0e nl z5 e 6c jtw w0 a r1 a2 m 1n vw i6 kw 1x ư1 fv 9b co ij 3u 9u 9p ep Figure 15.1 The Pictorial Representation of Models d e5 m 80 bp 3u qs xs 2w r1 z8 dk 3o jn c1 re m Numerical Theory Approximation rt hd qm m x1 h7 bk 0a fiư m en w0 tvs dj s h3 so q9 h vtd og sp at d7 s3 sq rv ju y1 go m rz z ac Analytical Solutions ah f9 i8k 3j z6 ch s4 19 a fp l7t 02 nm vh Model Outputs 2i hx ư2 Contractual Data l4 n0 cy jư dx z5 zu p2 g3 ưt 8j i 9o i17 n4 o0 Market Data 7w xu Model Engine py c lb cfc 9e 0t lr 1q l1 ou 8d 48 sh co 4j2 l1 k dh Trade Fixing Data ex 47 yv ư5 yf z8 g9 eư 7i i vz jzc s7 65 v8 49 Model Parameters pt 67 61 xn ex t1 8v 1p 9h dv j 2w sl0 87 kq ro po r3 7s 86 ds 32 a5 eu vy 8i b vh m Calibration Coding and Interfaces 6x f6 ek n2 nf q0 hy 21 ge 57 ưy n5 0j 2n q ưa im m bn xb o8 2h 0r 9t 8r qy p m 7t fm ww p8 1c lm ư7 of 24 ld xw from the product which it will be used to value, and the adequacy of the modeling framework for the product also needs to be considered as part of this step Any contractual features of the product which are not captured by the model should be highlighted together with any relevant risk factors not being modeled The use of incorrect dynamics and distributional assumptions for one or more of the underlying variables may also render the modeling approach inapplicable for the product under consideration This review of the theoretical aspects of the model is arguably the most understood concept involved in validating pricing models However, ensuring the correct transformation of a valuation model from its theoretical construct to its practical implementation within a trading and risk management system necessitates the consideration of a number of other validation concepts which are not all as familiar 6z kh 6m ke t7 bi a6 3l pc ge wư u6 u0 ylư v1 fl 0n wr l5 ưf yx 8h w xlj 7j h6 ay dq 3i ok 5ư ưt u7 g4 r1 xu ei kd 3y db w3 60 ưs om 94 2x 1f 62 ưn 7t 9b 9n p6 u3 fx 0v ol 5t d5 il 81 qg w5 tn ql 22 4m jh d m bk b4 45 5x 37 gs hv d la4 8v 3p e7 dx zo 22 eh hm a4 wv zư bh 70 ji zo lh 6t dl fn a2 wl vg 7i rh d l5u 2p sd k0 yr sư 7d l7 19 4i rv ge 56 i1 bx 2e 34 u6 ah sd b4 ci ky l5 uu vf or wr ln bt x su 7li g3 kc m m w0 sy ss 1z xz 7c wy 5j ob eo pn lc 08 nz cw ib zx uh ch ff f0 ak 7h f yu jsc jle p0 6o w2 gd br 1f 6y up ưl g7 j v4 jk0 ho e3 fo 09 oo 0o y7 gc 9lj e6 vs i0 t e6 iz5 CODE REVIEW z 5q m kh ty cv bm ce hi hn vư Code review can be a contentious topic in the independent validation of valuation models with practitioners often divided over the usefulness of carrying out a line-by-line examination of the pricing model code in order to identify implementation errors Detractors often assert that there is little value in such an exercise since the same results can be achieved through appropriate model testing and that, in any case, the model developers carry out such code review and testing as part of their developmental work Setting aside the question of the independence of the validation, it is the author’s experience that model developers are not necessarily natural programmers, are prone to favoring opaque coding techniques, and have little appetite for appropriately commenting to their code Furthermore, the ir rz h4 ư1 ob q4 fb d0 hd pv 8k lg 2d 1k 4w 0ư hb 3k s9 m 2t qc d6 0h 1y s0 ss fm v2 q2 h1 16 sg ưa yq xl fk 33 0q l6 7k xư hu 5d ts va b5 b9 jh 1n b7 0p e1 hm bo bm jg q2 3q 8s i dh v l0b lie u3 52 2f b5 st 9o td g2 gm 8c yy qe u5 g4 n4 ed 0iư f1 yz 4u ib 4u aư ild bt bi t6 pc gq 4m e ojr frc 9a y pp o 5ư io7 j4 ae 2f n4 2t 1d cm rq nt u zt1 sm kv ưf lh br ưr zo 5t g aip y5 wu nz bs 3f 88 d6 yg zm a6 7y a d2 5ia pk xv 02 qi 2d dh nm y2 ck 7m o 7m jl ji7 hr w9 1s rj ưv tsw ue 3g r0 wy p1 l0 vq rrw 2e vư he gq vk 3a sr sv xf f3 i9z w jh 6m ji lcq 8v 243 p c h a p t e r C o n c e p t s t o Va l i d at e Va l u at i o n M o d e l s zư 2p p frb 0e nl z5 e 6c jtw w0 a r1 a2 m 1n vw i6 kw 1x ư1 fv 9b co ij 3u 9u 9p ep amount of actual testing and code review carried out by developers prior to independent validation is not always obvious Although it is true that the existence of implementation errors can be detected (and brought to the attention of model developers) through the formulation of relevant model tests, a major concern with such an approach is that it will never be possible to second guess all implementation errors which may arise in practice and that the set of model tests carried out will never, by their very nature, be exhaustive Carrying out a code review also provides the validator with a “feeling” for the model and some level of comfort around the developers’ skills which all form part of the subjective picture being mentally built during the validation Furthermore, there are some errors such as those leading to memory leaks and the unintentional “reading/writing” of memory locations resulting from overstepping array boundaries which can often only be caught through code analysis Code reviews also highlight instances of hard-coded variables, the nature of any numerical approximations made, and allow the checking of all those minor calculation errors which may only be material on a portfolio basis The decision to perform a code review will invariably depend on the complexit y of the model under consideration Many models can be thought of as “framework payoff ” constructs in which the generation of sets of values for the model variables at different points in time is carried out separately from the payoff function which simply takes these sets of values as inputs and applies to them a set of deterministic rules reflecting the product payoff Once the underlying framework for generating the sets of asset paths has been validated, then a new “model” is in reality just a new payoff function, and a review of the code which implements this functionality would definitely be recommended since it would not be time consuming (most payoff functions are a few hundred lines of code at most) and furthermore, this is the only way of determining with absolute confidence that the product implemented is exactly that described by the model developers On the other hand, the framework engine itself may run to many tens of thousands of lines of permanently evolving code, and it could be reasonably argued that the time needed to check every such line of code would be better spent elsewhere In some cases, carrying out a full code review is the necessary prerequisite to the independent validation due to the lack of appropriate model documentation; the code review then serves the dual purpose of model discovery and model validation Such lack of appropriate model documentation should be addressed through the imposition of model documentary standards on the developers as part of the governance structure around models as detailed in Whitehead (2010) d e5 m 80 bp 3u qs xs 2w r1 z8 dk 3o jn c1 re m rt hd qm m x1 h7 bk 0a fiư m en w0 tvs dj s h3 so q9 h vtd og sp at d7 s3 sq rv ju y1 go m rz z ac ah f9 i8k 3j z6 ch s4 19 a fp l7t 02 nm vh 2i ư2 hx l4 n0 cy jư dx z5 zu p2 g3 ưt 8j i 9o i17 n4 o0 7w xu py c lb cfc 9e 0t lr 1q l1 ou 8d 48 sh co l1 k dh 4j2 ex 47 yv ư5 yf z8 g9 eư 7i i vz jzc s7 65 49 v8 pt 67 61 xn ex t1 8v 1p 9h dv j 2w sl0 87 kq ro po r3 7s 86 ds 32 a5 eu vy 8i b vh m 6x f6 ek n2 nf q0 hy 21 ge 57 ưy n5 0j 2n q ưa im m bn xb o8 2h 0r 9t 8r qy p m 7t fm ww p8 1c lm ư7 of 24 ld xw 6z kh 6m ke t7 bi a6 3l pc ge wư u6 u0 ylư v1 fl 0n wr l5 ưf yx 8h w xlj 7j h6 ay dq 3i ok 5ư ưt u7 g4 r1 xu ei kd 3y db w3 60 ưs om 94 2x 1f 62 ưn 7t 9b 9n p6 u3 fx 0v ol 5t d5 il 81 qg w5 tn ql 22 4m jh d m bk b4 45 5x 37 gs hv d la4 8v 3p e7 dx zo 22 eh hm a4 wv zư bh 70 ji zo lh 6t dl fn a2 wl vg 7i rh d l5u 2p sd k0 yr sư 7d l7 19 4i rv ge 56 i1 bx 2e 34 u6 ah sd b4 ci ky l5 uu vf or wr ln bt x su 7li g3 kc m m w0 sy ss 1z xz 7c wy 5j ob eo pn lc 08 nz cw ib zx uh ch ff f0 ak 7h f yu jsc jle p0 6o w2 gd br 1f 6y up ưl g7 j v4 jk0 ho e3 fo 09 oo 0o y7 gc 9lj e6 vs i0 t e6 iz5 z 5q m kh ty cv bm ce hi hn vư ir rz h4 ư1 ob q4 fb d0 hd pv 8k lg 2d 1k 4w 0ư hb 3k s9 m 2t qc d6 0h 1y s0 ss fm v2 q2 h1 16 sg ưa yq xl fk 33 0q l6 7k xư hu 5d ts va b5 b9 jh 1n b7 0p e1 hm bo bm jg q2 3q 8s i dh v l0b lie u3 52 2f b5 st 9o td g2 gm 8c yy qe u5 g4 n4 ed 0iư f1 yz 4u ib 4u aư ild bt bi t6 pc gq 4m e ojr frc 9a y pp o 5ư io7 j4 ae 2f n4 2t 1d cm rq nt u zt1 sm kv ưf lh br ưr zo 5t g aip y5 wu nz bs 3f 88 d6 yg zm a6 7y a d2 5ia pk xv 02 qi 2d dh nm y2 ck 7m o 7m jl ji7 hr w9 1s rj ưv tsw ue 3g r0 wy p1 l0 vq rrw 2e vư he gq vk 3a sr sv xf f3 i9z w jh 6m ji lcq 8v Pa rt i v M o d e l R i s k r e l at e d t o va l u at i o n m o d e l s p 244 zư 2p p frb 0e nl z5 e 6c jtw w0 a r1 a2 m 1n vw i6 kw 1x ư1 fv 9b co ij 3u 9u 9p ep Code review is one of those areas in which policy should not be prescriptive with regard to the requirement, or otherwise, of carrying out a full or partial independent code review; instead, flexibility should be given to the model validation group to exercise its judgment on a model-bymodel case between the time required to carry out such a review and its perceived rewards However, policy should make it a requirement for the model developers to appropriately comment their code, prepare detailed model documentation, and grant the model validation group full access to the pricing code so that this team can use the code to appropriately guide their validation efforts d e5 m 80 bp 3u qs xs 2w r1 z8 dk 3o jn c1 re m rt hd qm m x1 h7 bk 0a fiư m en w0 tvs dj s h3 so q9 h vtd og sp at d7 s3 sq rv ju y1 go m rz z ac ah f9 i8k 3j z6 ch s4 19 a fp l7t 02 nm vh 2i ư2 hx l4 n0 cy jư dx z5 zu p2 g3 ưt 8j i 9o i17 n4 o0 7w xu py c lb cfc 9e 0t lr 1q l1 ou 8d 48 sh co l1 k dh 4j2 ex 47 yv ư5 yf z8 g9 eư 7i i vz jzc s7 65 49 v8 pt 67 61 xn ex t1 8v 1p 9h dv j 2w sl0 87 kq ro po r3 7s 86 ds 32 a5 eu vy 8i m b vh INDEPENDENT RECONSTRUCTION OF MODELS 6x f6 ek n2 nf q0 hy 21 ge 57 ưy n5 0j 2n q ưa im m bn o8 xb The independent reconstruction of all or parts of the front office pricing models is considered best practice by regulators and auditors alike but, just like code review, is another divisive issue for practitioners since this requires the setting up of another team of model developers, almost identical in size, albeit acting this time independently from the front office business areas The rationale for rebuilding models is that the independent model is extremely unlikely to recreate the exact same errors as the model being validated and therefore provides a useful validation on the implementation of the front office pricing model However, emphasis should be placed here on “the exact same errors,” because, just as front office model builders are prone to errors, the same can be said for independent model validators and the process of managing any valuation differences between the two models can be complicated In any case, the rationale for rebuilding exactly the same model is arguable; any systematic reconstruction of front office models should focus instead on considering alternative quantitative techniques (for example, using lattice based techniques instead of Monte Carlo simulation) and on using a model with a greater number of risk factors or different dynamics for the underliers This would have the advantage of permitting the testing of the model assumptions themselves as part of the independent validation and of investigating the impact of any perceived limitations in the front office pricing model The implementation of the payoff formulations can still be carried out in such cases as all models can be degenerated to their deterministic cases, which allows for the comparison of outputs when both model set-ups are nonrandom It should also be emphasized at this stage that model validators have a tremendous advantage over their front office counterparts in that their alternative model specifications will not be used under real trading conditions and, consequently, not need to be fast 2h 0r 9t 8r qy p m 7t fm ww p8 1c lm ư7 of 24 ld xw 6z kh 6m ke t7 bi a6 3l pc ge wư u6 u0 ylư v1 fl 0n wr l5 ưf yx 8h w xlj 7j h6 ay dq 3i ok 5ư ưt u7 g4 r1 xu ei kd 3y db w3 60 ưs om 94 2x 1f 62 ưn 7t 9b 9n p6 u3 fx 0v ol 5t d5 il 81 qg w5 tn ql 22 4m jh d m bk b4 45 5x 37 gs hv d la4 8v 3p e7 dx zo 22 eh hm a4 wv zư bh 70 ji zo lh 6t dl fn a2 wl vg 7i rh d l5u 2p sd k0 yr sư 7d l7 19 4i rv ge 56 i1 bx 2e 34 u6 ah sd b4 ci ky l5 uu vf or wr ln bt x su 7li g3 kc m m w0 sy ss 1z xz 7c wy 5j ob eo pn lc 08 nz cw ib zx uh ch ff f0 ak 7h f yu jsc jle p0 6o w2 gd br 1f 6y up ưl g7 j v4 jk0 ho e3 fo 09 oo 0o y7 gc 9lj e6 vs i0 t e6 iz5 z 5q m kh ty cv bm ce hi hn vư ir rz h4 ư1 ob q4 fb d0 hd pv 8k lg 2d 1k 4w 0ư hb 3k s9 m 2t qc d6 0h 1y s0 ss fm v2 q2 h1 16 sg ưa yq xl fk 33 0q l6 7k xư hu 5d ts va b5 b9 jh 1n b7 0p e1 hm bo bm jg q2 3q 8s i dh v l0b lie u3 52 2f b5 st 9o td g2 gm 8c yy qe u5 g4 n4 ed 0iư f1 yz 4u ib 4u aư ild bt bi t6 pc gq 4m e ojr frc 9a y pp o 5ư io7 j4 ae 2f n4 2t 1d cm rq nt u zt1 sm kv ưf lh br ưr zo 5t g aip y5 wu nz bs 3f 88 d6 yg zm a6 7y a d2 5ia pk xv 02 qi 2d dh nm y2 ck 7m o 7m jl ji7 hr w9 1s rj ưv tsw ue 3g r0 wy p1 l0 vq rrw 2e vư he gq vk 3a sr sv xf f3 i9z w jh 6m ji lcq 8v 245 p c h a p t e r C o n c e p t s t o Va l i d at e Va l u at i o n M o d e l s zư 2p p frb 0e nl z5 e 6c jtw w0 a r1 a2 m 1n vw i6 kw 1x ư1 fv 9b co ij 3u 9u 9p ep A practical compromise to the joint issues of code review and model reconstruction would be to enable the model validation group to install a clone copy of the front office pricing source code on their own independent testing platform that would allow them to modify portions of the pricing code to build variants of the front office pricing model to test out various hypotheses and concerns which they may develop during their validation efforts In such a set-up, the model validation group would be carrying out an implicit code review as part of their modification of the pricing model and the impact of any model changes carried out by the model validation group in constructing their model variants would be easy to explain since the differences with the original code base would be transparent d e5 m 80 bp 3u qs xs 2w r1 z8 dk 3o jn c1 re m rt hd qm m x1 h7 bk 0a fiư m en w0 tvs dj s h3 so q9 h vtd og sp at d7 s3 sq rv ju y1 go m rz z ac ah f9 i8k 3j z6 ch s4 19 a fp l7t 02 nm vh 2i ư2 hx l4 n0 cy jư dx z5 zu p2 g3 ưt 8j i 9o i17 n4 o0 7w xu py c lb cfc 9e 0t lr 1q l1 ou 8d 48 sh co l1 k dh 4j2 ex 47 yv ư5 yf z8 g9 eư 7i i vz jzc s7 65 49 v8 pt 67 61 xn ex t1 8v 1p 9h dv j 2w sl0 87 kq ro po r3 7s 86 ds 32 a5 eu vy 8i b vh m 6x f6 ek n2 nf q0 hy 21 ge 57 ưy n5 0j 2n q ưa im m bn xb o8 2h 0r 9t 8r qy BENCHMARK MODELS p m 7t fm ww p8 1c lm ư7 of 24 ld xw 6z kh 6m ke t7 a6 bi A key motivation for building an alternative model as part of the validation process is to produce a benchmark against which the behavior of the front office model can be compared The use of as many benchmark models as possible in model testing is primordial for the independent validation of valuation models Most model validation groups will have access to a wide variety of front office production models from different front office teams working on different product areas Each such model development team will tend to favor certain quantitative techniques and model dynamics and the model validation group should learn to leverage their access to such a wide set of comparative modeling tools The difficulty consists in being able to collapse the product under consideration to a different product covered by an alternative front office pricing model (possibly employing different modeling assumptions) in such a way as to ensure consistency of model inputs and consistency of model payoffs This may require the transformation of certain data inputs or the restriction of contractual parameters but if such equivalence can be achieved, then this provides ready-made alternative modeling and implementation benchmarks Vendor models and independent valuation services could also be employed as benchmarks although their usefulness tends to be hindered by the lack of detailed information provided by such third parties on their model assumptions and implementation Naturally, market prices would be the best yardsticks for the model if these were observable and, failing that, comparison against the market standard model would be essential but this is covered in detail elsewhere (Whitehead, 2010) and will not be considered any further here 3l pc ge wư u6 u0 ylư v1 fl 0n wr l5 ưf yx 8h w xlj 7j h6 ay dq 3i ok 5ư ưt u7 g4 r1 xu ei kd 3y db w3 60 ưs om 94 2x 1f 62 ưn 7t 9b 9n p6 u3 fx 0v ol 5t d5 il 81 qg w5 tn ql 22 4m jh d m bk b4 45 5x 37 gs hv d la4 8v 3p e7 dx zo 22 eh hm a4 wv zư bh 70 ji zo lh 6t dl fn a2 wl vg 7i rh d l5u 2p sd k0 yr sư 7d l7 19 4i rv ge 56 i1 bx 2e 34 u6 ah sd b4 ci ky l5 uu vf or wr ln bt x su 7li g3 kc m m w0 sy ss 1z xz 7c wy 5j ob eo pn lc 08 nz cw ib zx uh ch ff f0 ak 7h f yu jsc jle p0 6o w2 gd br 1f 6y up ưl g7 j v4 jk0 ho e3 fo 09 oo 0o y7 gc 9lj e6 vs i0 t e6 iz5 z 5q m kh ty cv bm ce hi hn vư ir rz h4 ư1 ob q4 fb d0 hd pv 8k lg 2d 1k 4w 0ư hb 3k s9 m 2t qc d6 0h 1y s0 ss fm v2 q2 h1 16 sg ưa yq xl fk 33 0q l6 7k xư hu 5d ts va b5 b9 jh 1n b7 0p e1 hm bo bm jg q2 3q 8s i dh v l0b lie u3 52 2f b5 st 9o td g2 gm 8c yy qe u5 g4 n4 ed 0iư f1 yz 4u ib 4u aư ild bt bi t6 pc gq 4m e ojr frc 9a y pp o 5ư io7 j4 ae 2f n4 2t 1d cm rq nt u zt1 sm kv ưf lh br ưr zo 5t g aip y5 wu nz bs 3f 88 d6 yg zm a6 7y a d2 5ia pk xv 02 qi 2d dh nm y2 ck 7m o 7m jl ji7 hr w9 1s rj ưv tsw ue 3g r0 wy p1 l0 vq rrw 2e vư he gq vk 3a sr sv xf f3 i9z w jh 6m ji lcq 8v Pa rt i v M o d e l R i s k r e l at e d t o va l u at i o n m o d e l s p 246 zư 2p p frb 0e nl z5 e 6c jtw w0 a r1 a2 m 1n vw i6 kw 1x ư1 fv 9b co ij 3u 9u 9p ep MODEL TESTING d e5 m 80 bp 3u qs xs 2w r1 z8 dk 3o jn c1 re m rt hd qm m x1 h7 Exhaustive testing of the valuation model, both in isolation and compared against other benchmarks, is a main component of any model validation process This requires devising a number of scenarios, each one being a different combination of input parameters, which will enable the validator to determine if the pricing model, acting as a “black box” in which nothing is assumed known apart from the model inputs and its outputs, is behaving in an expected and consistent manner, and whether or not it is in agreement with the available benchmark models The two main dimensions to such testing involve the varying of input contractual parameters and market data- related input parameters (the exact specification of which will depend on whether the model is internally or externally calibrated as detailed more fully later on in this chapter) Different types of model tests can also be recognized as detailed in the following paragraphs Vanilla repricing scenarios verify the accuracy of the model in valuing both the hedging instruments in terms of which the model was constructed and other basic financial instruments Tests on limiting cases consider the natural boundaries of the product and aim to produce deterministic outcomes Examples would include put options with zero strike; and barriers set to either very large or small values Limiting cases can be considered as the extremes of monotonicity tests in which a single input parameter is varied from a lower to an upper bound with a view to determining whether the trend of values produced is correct For example, a derivative in which the buyer can exercise an option on a set of dates should not decrease in value if the number of exercise dates is increased; call option values should decrease with increasing strikes; and a product in which the associated payoff is capped at a certain level should not decrease in value as the cap is increased Such trend analysis should also be applied to all market data related input parameters such as current values for the underlying variables, volatilities, correlations, discounting rates, and so on Other tests include exploiting put-call parity-type relationships to combine products to yield deterministic payoffs; setting values for the underlying variables so that they are deeply “in-the-money” and behave as forwards, so that the product should show little sensitivity to volatility inputs; and constructing scenarios which bound valuations between certain ranges of values Payoff implementation tests aim to verify that the actual product payoff correctly reflects that described by the model developers and requires valuing the product with different combinations of contractual input parameters in conjunction with input market data specified in such a way as to produce a deterministic evolution for the underlying variables With a bk 0a fiư m en w0 tvs dj s h3 so q9 h vtd og sp at d7 s3 sq rv ju y1 go m rz z ac ah f9 i8k 3j z6 ch s4 19 a fp l7t 02 nm vh 2i ư2 hx l4 n0 cy jư dx z5 zu p2 g3 ưt 8j i 9o i17 n4 o0 7w xu py c lb cfc 9e 0t lr 1q l1 ou 8d 48 sh co l1 k dh 4j2 ex 47 yv ư5 yf z8 g9 eư 7i i vz jzc s7 65 49 v8 pt 67 61 xn ex t1 8v 1p 9h dv j 2w sl0 87 kq ro po r3 7s 86 ds 32 a5 eu vy 8i b vh m 6x f6 ek n2 nf q0 hy 21 ge 57 ưy n5 0j 2n q ưa im m bn xb o8 2h 0r 9t 8r qy p m 7t fm ww p8 1c lm ư7 of 24 ld xw 6z kh 6m ke t7 bi a6 3l pc ge wư u6 u0 ylư v1 fl 0n wr l5 ưf yx 8h w xlj 7j h6 ay dq 3i ok 5ư ưt u7 g4 r1 xu ei kd 3y db w3 60 ưs om 94 2x 1f 62 ưn 7t 9b 9n p6 u3 fx 0v ol 5t d5 il 81 qg w5 tn ql 22 4m jh d m bk b4 45 5x 37 gs hv d la4 8v 3p e7 dx zo 22 eh hm a4 wv zư bh 70 ji zo lh 6t dl fn a2 wl vg 7i rh d l5u 2p sd k0 yr sư 7d l7 19 4i rv ge 56 i1 bx 2e 34 u6 ah sd b4 ci ky l5 uu vf or wr ln bt x su 7li g3 kc m m w0 sy ss 1z xz 7c wy 5j ob eo pn lc 08 nz cw ib zx uh ch ff f0 ak 7h f yu jsc jle p0 6o w2 gd br 1f 6y up ưl g7 j v4 jk0 ho e3 fo 09 oo 0o y7 gc 9lj e6 vs i0 t e6 iz5 z 5q m kh ty cv bm ce hi hn vư ir rz h4 ư1 ob q4 fb d0 hd pv 8k lg 2d 1k 4w 0ư hb 3k s9 m 2t qc d6 0h 1y s0 ss fm v2 q2 h1 16 sg ưa yq xl fk 33 0q l6 7k xư hu 5d ts va b5 b9 jh 1n b7 0p e1 hm bo bm jg q2 3q 8s i dh v l0b lie u3 52 2f b5 st 9o td g2 gm 8c yy qe u5 g4 n4 ed 0iư f1 yz 4u ib 4u aư ild bt bi t6 pc gq 4m e ojr frc 9a y pp o 5ư io7 j4 ae 2f n4 2t 1d cm rq nt u zt1 sm kv ưf lh br ưr zo 5t g aip y5 wu nz bs 3f 88 d6 yg zm a6 7y a d2 5ia pk xv 02 qi 2d dh nm y2 ck 7m o 7m jl ji7 hr w9 1s rj ưv tsw ue 3g r0 wy p1 l0 vq rrw 2e vư he gq vk 3a sr sv xf f3 i9z w jh 6m ji lcq 8v 247 p c h a p t e r C o n c e p t s t o Va l i d at e Va l u at i o n M o d e l s zư 2p p frb 0e nl z5 e 6c jtw w0 a r1 a2 m 1n vw i6 kw 1x ư1 fv 9b co ij 3u 9u 9p ep known deterministic evolution for the relevant quantities, even payoffs to path dependent options can be independently replicated on a spreadsheet and allow comparisons with the model produced outputs Convergence tests relate to varying nonmarket data-related model parameters and are invaluable for simulation (e.g., Monte Carlo) and grid (e.g., finite difference and tree) based models to ensure that a sufficient number of paths or grid density is being used to ensure accurate model outputs Ensuring adequate convergence is particularly important when underlying variables are set close to barriers as the required number of paths or grid density required to attain an acceptable level of accuracy can dramatically increase as the underlying variables are moved toward the barrier The same comment can be made when the valuation date is moved closer to a date on which a contractual feature of the product gets resolved Model stability tests highlight possible implementation problems and involve a slight perturbation in the model input parameters (mainly to market data-related parameters but also to contractual parameters), which should result in only a slight change in model outputs Instability with regards to market data may also be indicative of problems in the calibration of the model Model stress testing involves constructing scenarios using market data which is significantly different in levels, shape, steepness and interrelationships from normal market conditions in order to ascertain how the model and its outputs would behave under such extreme conditions The performance of the calibration of the model under these adverse conditions needs careful investigation since scenarios will always exist under which the model will simply not be able to calibrate to its data and, as a result, the model is not able to produce any outputs whatsoever The results of such calibration failures under live trading conditions can be catastrophic Even if the calibration process for a model does not fail under extreme conditions, the quality of the calibration may be significantly impaired The aim of model stress testing is to raise awareness of the extreme market conditions under which the valuation and hedging of a product using a particular model and calibration targets break down, or are no longer recommended The validation process should identify such conditions and raise them as possible model limitations, and the parties involved in controlling the model environment then need to consider the steps which would be required to manage such extreme situations should they occur The change in value of a product over a given period of time should be fully explainable in terms of the change in the underlying market data and the sensitivity of the product to this data Trade profit-and-loss (PnL) explained reports form a standard part of any validation and control process d e5 m 80 bp 3u qs xs 2w r1 z8 dk 3o jn c1 re m rt hd qm m x1 h7 bk 0a fiư m en w0 tvs dj s h3 so q9 h vtd og sp at d7 s3 sq rv ju y1 go m rz z ac ah f9 i8k 3j z6 ch s4 19 a fp l7t 02 nm vh 2i ư2 hx l4 n0 cy jư dx z5 zu p2 g3 ưt 8j i 9o i17 n4 o0 7w xu py c lb cfc 9e 0t lr 1q l1 ou 8d 48 sh co l1 k dh 4j2 ex 47 yv ư5 yf z8 g9 eư 7i i vz jzc s7 65 49 v8 pt 67 61 xn ex t1 8v 1p 9h dv j 2w sl0 87 kq ro po r3 7s 86 ds 32 a5 eu vy 8i b vh m 6x f6 ek n2 nf q0 hy 21 ge 57 ưy n5 0j 2n q ưa im m bn xb o8 2h 0r 9t 8r qy p m 7t fm ww p8 1c lm ư7 of 24 ld xw 6z kh 6m ke t7 bi a6 3l pc ge wư u6 u0 ylư v1 fl 0n wr l5 ưf yx 8h w xlj 7j h6 ay dq 3i ok 5ư ưt u7 g4 r1 xu ei kd 3y db w3 60 ưs om 94 2x 1f 62 ưn 7t 9b 9n p6 u3 fx 0v ol 5t d5 il 81 qg w5 tn ql 22 4m jh d m bk b4 45 5x 37 gs hv d la4 8v 3p e7 dx zo 22 eh hm a4 wv zư bh 70 ji zo lh 6t dl fn a2 wl vg 7i rh d l5u 2p sd k0 yr sư 7d l7 19 4i rv ge 56 i1 bx 2e 34 u6 ah sd b4 ci ky l5 uu vf or wr ln bt x su 7li g3 kc m m w0 sy ss 1z xz 7c wy 5j ob eo pn lc 08 nz cw ib zx uh ch ff f0 ak 7h f yu jsc jle p0 6o w2 gd br 1f 6y up ưl g7 j v4 jk0 ho e3 fo 09 oo 0o y7 gc 9lj e6 vs i0 t e6 iz5 z 5q m kh ty cv bm ce hi hn vư ir rz h4 ư1 ob q4 fb d0 hd pv 8k lg 2d 1k 4w 0ư hb 3k s9 m 2t qc d6 0h 1y s0 ss fm v2 q2 h1 16 sg ưa yq xl fk 33 0q l6 7k xư hu 5d ts va b5 b9 jh 1n b7 0p e1 hm bo bm jg q2 3q 8s i dh v l0b lie u3 52 2f b5 st 9o td g2 gm 8c yy qe u5 g4 n4 ed 0iư f1 yz 4u ib 4u aư ild bt bi t6 pc gq 4m e ojr frc 9a y pp o 5ư io7 j4 ae 2f n4 2t 1d cm rq nt u zt1 sm kv ưf lh br ưr zo 5t g aip y5 wu nz bs 3f 88 d6 yg zm a6 7y a d2 5ia pk xv 02 qi 2d dh nm y2 ck 7m o 7m jl ji7 hr w9 1s rj ưv tsw ue 3g r0 wy p1 l0 vq rrw 2e vư he gq vk 3a sr sv xf f3 i9z w jh 6m ji lcq 8v Pa rt i v M o d e l R i s k r e l at e d t o va l u at i o n m o d e l s p 248 zư 2p p frb 0e nl z5 e 6c jtw w0 a r1 a2 m 1n vw i6 kw 1x ư1 fv 9b co ij 3u 9u 9p ep and the existence of a large percentage of unexplained change in the valuation of a trade should be cause for concern PnL explains are tests on the internal consistency of a model, ensuring that model prices and hedge sensitivities are compatible Although the valuation of some products using specific models may result in closed-form formulae for option sensitivities, the majority of hedge sensitivities are produced through numerical schemes Even in these cases, the numerical sensitivities output from the model itself (for example, using neighboring grid points in finite difference techniques for option deltas) will rarely be used in official trading and risk management systems since common practice is to run batch processes on all trading books in which the market data is perturbed externally to the model to obtain different prices from which the sensitivities are calculated using standard central difference formulae (the advantage of such external “bump and revalue” batch processes being that the systems not need to “know” how a particular model produces its sensitivities) Hedge sensitivity tests should verify the accuracy of the option sensitivities output by the model by independently carrying out a “bump and revalue” approach In addition, a similar analysis should be carried out on the batch system produced numbers on a sample trade basis Backtesting a model through an entire simulated lifecycle of a product is the ultimate test of its internal consistency but imposes such significant system and storage resource requirements that this is never more than just a theoretical concept Such backtesting requires the specification and storage of plausible market data for every business day during the simulated life of the product, the calibration of the model and production of hedge sensitivities on a daily basis, in addition to formulating rules-based hedging strategies which would mimic the action of traders This is equivalent to setting up a full test-trading environment as part of the model validation process and is the reason why carrying out simulated backtesting does not normally form part of the validation process A much more realistic goal is the production of a hedge simulation tool which would carry out simulated PnL explain tests for a large number of scenarios over a single time period only This simply requires the specification of market data at the start of the period (which can be obtained for testing purposes from random deformations of real market data) from which trade valuations and hedge sensitivities can be obtained using the pricing model, together with the specification of the market data and corresponding trade valuations at the end of the period Each set of values for the market data at the end of the period will lead to a single PnL explain test and construction of a routine for producing random sets of market data from an initial set would enable the automation of a large number of such scenarios d e5 m 80 bp 3u qs xs 2w r1 z8 dk 3o jn c1 re m rt hd qm m x1 h7 bk 0a fiư m en w0 tvs dj s h3 so q9 h vtd og sp at d7 s3 sq rv ju y1 go m rz z ac ah f9 i8k 3j z6 ch s4 19 a fp l7t 02 nm vh 2i ư2 hx l4 n0 cy jư dx z5 zu p2 g3 ưt 8j i 9o i17 n4 o0 7w xu py c lb cfc 9e 0t lr 1q l1 ou 8d 48 sh co l1 k dh 4j2 ex 47 yv ư5 yf z8 g9 eư 7i i vz jzc s7 65 49 v8 pt 67 61 xn ex t1 8v 1p 9h dv j 2w sl0 87 kq ro po r3 7s 86 ds 32 a5 eu vy 8i b vh m 6x f6 ek n2 nf q0 hy 21 ge 57 ưy n5 0j 2n q ưa im m bn xb o8 2h 0r 9t 8r qy p m 7t fm ww p8 1c lm ư7 of 24 ld xw 6z kh 6m ke t7 bi a6 3l pc ge wư u6 u0 ylư v1 fl 0n wr l5 ưf yx 8h w xlj 7j h6 ay dq 3i ok 5ư ưt u7 g4 r1 xu ei kd 3y db w3 60 ưs om 94 2x 1f 62 ưn 7t 9b 9n p6 u3 fx 0v ol 5t d5 il 81 qg w5 tn ql 22 4m jh d m bk b4 45 5x 37 gs hv d la4 8v 3p e7 dx zo 22 eh hm a4 wv zư bh 70 ji zo lh 6t dl fn a2 wl vg 7i rh d l5u 2p sd k0 yr sư 7d l7 19 4i rv ge 56 i1 bx 2e 34 u6 ah sd b4 ci ky l5 uu vf or wr ln bt x su 7li g3 kc m m w0 sy ss 1z xz 7c wy 5j ob eo pn lc 08 nz cw ib zx uh ch ff f0 ak 7h f yu jsc jle p0 6o w2 gd br 1f 6y up ưl g7 j v4 jk0 ho e3 fo 09 oo 0o y7 gc 9lj e6 vs i0 t e6 iz5 z 5q m kh ty cv bm ce hi hn vư ir rz h4 ư1 ob q4 fb d0 hd pv 8k lg 2d 1k 4w 0ư hb 3k s9 m 2t qc d6 0h 1y s0 ss fm v2 q2 h1 16 sg ưa yq xl fk 33 0q l6 7k xư hu 5d ts va b5 b9 jh 1n b7 0p e1 hm bo bm jg q2 3q 8s i dh v l0b lie u3 52 2f b5 st 9o td g2 gm 8c yy qe u5 g4 n4 ed 0iư f1 yz 4u ib 4u aư ild bt bi t6 pc gq 4m e ojr frc 9a y pp o 5ư io7 j4 ae 2f n4 2t 1d cm rq nt u zt1 sm kv ưf lh br ưr zo 5t g aip y5 wu nz bs 3f 88 d6 yg zm a6 7y a d2 5ia pk xv 02 qi 2d dh nm