The Hong Kong University of Science and Technology
Computational Methods for Pricing Structured Products
MAFS 5250

Fall 2014
MAFS5250 Computational Methods for Pricing Structured
Products
Topic 4  Monte Carlo simulation
4.1 General formulation of the Monte Carlo procedure
Expected value and variance of the estimate
Multistate extension correlated random samples
Computationa
The Hong Kong University of Science and Technology
Computational Methods for Pricing Structured Products
MAFS 5250

Fall 2014
MAFS5250 Computational Methods for Pricing Structured Products
Topic 1 Lattice tree methods
1.1 Binomial option pricing models
From replication to risk neutral valuation
Continuous limit of the binomial model
Multiperiod extension
Dynamic programming
The Hong Kong University of Science and Technology
Computational Methods for Pricing Structured Products
MAFS 5250

Fall 2014
MAFS5250  Computational Methods for Pricing Structured Products
Homework One
Course instructor: Prof. Y.K. Kwok
1. Suppose the underlying asset is paying a continuous dividend yield at the rate q, the two
governing equations for u, d and p are modied as
The Hong Kong University of Science and Technology
Computational Methods for Pricing Structured Products
MAFS 5250

Fall 2014
MAFS5250  Computational Methods for Pricing Structured Products
Solution to Homework Two
Course instructor: Prof. Y.K. Kwok
1. Expand f(x0 2x) and f(x0 x) at x0 into Taylor series, where
f(x0 2x) = f(x0) 2xf (x0) + 4x2 f (x0 ) + O(x3 )
f(x0 x) = f(x0) xf
The Hong Kong University of Science and Technology
Computational Methods for Pricing Structured Products
MAFS 5250

Fall 2014
MAFS5250  Computational Methods for Pricing Structured Products
Homework Two
Course instructor: Prof. Y.K. Kwok
df
1. Suppose we would like to approximate
at x0 up to O(x2 ) using function values of f
dx
at x0 , x0 x and x 2x, the onesided backward dier
The Hong Kong University of Science and Technology
Computational Methods for Pricing Structured Products
MAFS 5250

Fall 2014
MAFS5250  Computational Methods for Pricing Structured Products
Solution to Homework One
Course instructor: Prof. Y.K. Kwok
1. When the underlying asset pays a continuous dividend yield at the rate q, the expected
rate of return of the asset is r q under
The Hong Kong University of Science and Technology
Computational Methods for Pricing Structured Products
MAFS 5250

Fall 2014
MAFS5250 Computational Methods for Pricing Structured
Products
Topic 2 Implied binomial trees and calibration of interest rate
trees
2.1 Implied binomial trees of tting market data of option prices
Some structures of the implied binomial trees
DermanKa
The Hong Kong University of Science and Technology
Computational Methods for Pricing Structured Products
MAFS 5250

Fall 2014
MAFS 5250
Computational Methods for Pricing Structured Products
Final Examination 2014 Spring
Time allowed: 3 hours
Course Instructor: Prof. Y. K. Kwok
[points]
1. Consider the CheukVorst algorithm for pricing oating strike lookback put options. The
trun