An Introduction to Financial Option Valuation Mathematics Stochastics and Computation 4 docx
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_13 pot
... O(h
4
). (23. 14)
23.7 Von Neumann stability and convergence 247
0
5
10
15
0
2
4
6
8
10
0
0.2
0 .4
0.6
0.8
1
x
BTCS: ν = 6.6
t
Fig. 23.7. BTCS solution on the heat equation (23.2), (23.3) and (23 .4) ... data ( 24. 2) or ( 24. 3) and the boundary values V
i
0
and V
i
N
x
for all 1 ≤ i ≤ N
t
specified by the boundary conditions ( 24. 4) or ( 24. 5).
To obtain a generalized vers...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_14 pot
... 60
true random numbers, 40
unbiased, 142 , 148
uniform distribution, 22, 24, 28
up -and- in call, 190, 223
up -and- in put, 190
up -and- out call, 190, 1 94, 195, 197
up -and- out put, 190
variance, 24, 142
variance ... neutrality, 115, 118–120, 144 , 146 , 151, 1 54, 163,
167, 180, 181, 1 94, 232
cash-or-nothing, 167–168
sample mean, 34, 48 , 64, 141 , 146 ,
2 04, 215
sample variance, 3...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_1 pot
... MathWorks, Inc.
AN INTRODUCTION TO FINANCIAL
OPTION VALUATION
Mathematics, Stochastics and Computation
This is a lively textbook providing a solid introduction to financial option valuation
for ... Chapter 24 and walkthrough 265
References 267
Index 271
viii Contents
4 Computer simulation 33
4. 1 Motivation 33
4. 2 Pseudo-random numbers 33
4. 3 Statistical te...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_3 pptx
... rand and
randn to generate U(0, 1) and N(0, 1) samples, respectively. To make the experiments reproducible, we set the
random number generator seed to 100; that is, we used rand(‘state’,100) and ... samples from N(0, 1) and U(0, 1) random number generators.
3
Random variables
OUTLINE
• discrete and continuous random variables
• expected value and variance
• uniform and nor...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_4 ppt
... way to compute a quantile–quantile plot, as seen in Figures 4. 4, 4. 6 and
5.3. It is listed in Figure 5 .4. We use MATLAB’s N(0, 1) pseudo-random number generator, randn.
The line samples = randn(M,1), ... known to investors, and hence any change in the price
is due to new information. We may build this into our model by adding a ran-
dom ‘fluctuation’ increment to the interest...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_5 ppt
... the
company and has many insights into the practical issues involved in collecting and
analysing vast amounts of financial data.
EXERCISES
7.1. Confirm the results (7 .4) and (7.5).
7.2. By analogy ... see (Rogers and Zane, 1999), for example.
A completely different approach is to abandon any attempt to understand the
processes that drive asset prices (in particular to pay n...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_7 pdf
... problem
and it is marvelously intuitive.
MARK P. KRITZMAN (Kritzman, 2000)
To put it simply,
if there is an arbitrage price, any other price is too dangerous to quote.
MARTIN BAXTER AND ANDREW ... prices, and counting the proportion
that are in-the-money.
P12.2. Investigate the use of
quad and quadl for evaluating integrals of the form
(12 .4) .
12 .4 Notes and references 119...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_8 pptx
... a and variance var(X) = b
2
are not known. Suppose
• we are interested in computing an approximation to a (and possibly b), and
• we are able to take independent samples of X using a pseudo-random ... From ( 14. 1) and ( 14. 2), values of C(σ ) must lie between
max(0, S − Ee
−r(T −t)
) and S.Itfollows that C(σ ) = C
has a solution if and
only if
max(S − Ee
−r(T −t)
, 0) ≤ C...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_9 pot
... 250
1 .46
1 .48
1.5
1.52
M
European put
200 220 240 260 280 300 320 340 360 380 40 0
1 .47 2
1 .47 3
1 .47 4
1 .47 5
1 .47 6
1 .47 7
M
European put
Fig. 16.2. Convergence of the binomial method for a European ... Chapter 8 that led to the
Black–Scholes PDE can be adapted to cover an American put option. We write
P
Am
(S, t) to denote the American put option value at asset price...
An Introduction to Financial Option Valuation Mathematics Stochastics and Computation_1 doc
... arguments to those above can be used to obtain simple upper and lower
bounds on the values C and P of European call and put options.
To study the call option, consider two portfolios:
π
A
: one call option ... than π
B
at time 0 then it would be possible to sell π
A
(that is, sell the call option and borrow the cash) and buy π
B
(that is, buy one put
option and one...
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