An Introduction to Financial Option Valuation_2 potx
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_13 pot
... in the matrix–vector forms (23.9) and (23.11), and
the Crank–Nicolson method is given by (24.8).
The τ = 0 condition (19.2) specifies V
0
j
= max(B + jh − E, 0) and the
left-hand boundary condition ... problem of valuing an American option can be
couched in terms of a linear complementarity problem. It is possible to develop
24.2 FTCS, BTCS and Crank–Nicolson for Black–Scholes 25...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_14 pot
... G. and E. J. Stapleton (1998) Fast accurate binomial pricing of options.
Finance and Stochastics, 2:3–17.
Rogers, L. C. G. and O. Zane (1999) Saddle-point approximations to option prices.
Annals ... Economic Dynamics and Control, 21:1267–1321.
Broadie, Mark and Paul Glasserman (1998) Introduction to Chapter III: Volatility and
correlation. In Mark Broadie and Paul Glass...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_1 pot
... The 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 ... Upper and lower bounds on option values 14
2.7 Notes and references 16
2.8 Program of Chapter 2 and walkthrough 17
3 Random variables 21
3.1 Motivation 21
3.2 Rando...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_3 pptx
... 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 normal distributions
• ... by i.i.d. random variables and hence
the overall effect can be reasonably modelled by a single normal random vari-
able with an appropriate mean and variance. This is why normal ran...
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 rate...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_5 ppt
... 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 no heed to the efficient ... 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...
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 ... is to scale the option values by the
asset price, by letting
c :=
C
S
, for a call option,
and
p :=
P
S
, for a put option.
In these new variables, d
1
and d
2
in (8.20) and (...
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 ... highly relevant is (Hammersley and Handscombe, 1964), whilst a short
and very accessible modern perspective is given by (Madras, 2002). Monte Carlo,
pseudo-random number generatio...
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_9 pot
... 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 S and time t, and
use (S(t)) ... the Black–Scholes analysis, places analytic formulas out of
reach, and puts a strain on computational methods.
18.2 American call and put
An American option is like a Eur...
An Introduction to Financial Option Valuation_1 potx
... sample means and variances approach the true
values 0 and 1.
A more enlightening approach to testing a random number generator is to divide
the x-axis into subintervals, or bins,oflength x and count ... by i.i.d. random variables and hence
the overall effect can be reasonably modelled by a single normal random vari-
able with an appropriate mean and variance. This is why normal random...
An Introduction to Financial Option Valuation_2 potx
... movement
The book (Lo and MacKinlay, 1999) is a good source of practical information for
stock market data analysis.
Many exchanges have informative websites, including the American Stock
Exchange: www.amex.com/, ... Stock
Exchange: www.amex.com/, the Chicago Board Options Exchange: www.
cboe.com/Home/, the London Stock Exchange: www.londonstockexchange.
com/, the New York Stock Exchange: www...
An Introduction to Financial Option Valuation_4 pot
... of us to carry
out hedging. On one side there is a large group of investors who view options as
an excellent means to alleviate their exposure to risk, and another large group who
see options ... rapidly, the Fed managed to persuade a consortium of major banks and in-
vestment houses to bail out LTCM in order to prevent the very real possibility of a
total meltdown of the financi...
An Introduction to Financial Option Valuation_6 ppt
... two
threads together and introduce the Monte Carlo approach to valuing an option.
As we will see in Chapter 19, this provides a powerful means to compute option
values in cases where no analytical ... showed that valuing an option can be regarded as computing an ex-
pected value. The idea of using pseudo-random number generators to compute
estimates of expected values was to...
An Introduction to Financial Option Valuation_8 pdf
... 19.6.
19.5 Bermudan and shout options
A Bermudan option differs from the corresponding American option in only one
respect. While the American option allows the holder to exercise at any time in
[0, ... deals with points (i) and (iii).
180 American options
18.6 Monte Carlo for an American put
We have seen that the binomial method has a natural extension from European to
American o...
An Introduction to Financial Option Valuation_9 doc
... σ
is computed in order to value an option, then a widely quoted rule of
thumb is to make the historical data time-frame Mt equal to that of the option:
to value an option that expires in six ... important aspects of practical
option valuation, and it remains an active research topic, see (Poon and Granger,
2003), for example.
More sophisticated time-varying volatility m...