City University of Hong Kong Department of Economics and Finance
Course EF5213 Assignment #2 ( due March 4, 2018 ) 1. Use VBA as programming tool, implement the implicit finite difference method under the Crank-
Nicholson scheme to price an accumulator contract written on a stock with Cox-Ingersoll-Ross volatility structure as (St, t) √St , where St is the underlying stock price at time t. Consider the following input parameters in your implementation :
On option :
r Risk free interest rate
Volatility factor of the underlying stock
Q Contract size
{ T1 , T2 , … , Tn } Settlement dates of the contract K Strike price of the contract
L Knock-out price of the contract
L K
St0
T1 T2 T3 … Tn
On precision : imax Number of steps to maturity
jmax Size parameter of the tridiagonal matrix
S Price increment in the lattice
To improve efficiency, use the enclosed SolveAxb routine from Numerical Recipies in solving the
matrix equation Ann xn1 bn1 based on singular value decomposition.
Note : With accumulator, investor agrees and also entitles to buy a certain amount Q of a stock at a fixed price K and at every settlement dates { T1 , T2 , … , Tn } over a period of time. There is a knock-out price (L K) that terminates the contract.
Define time steps ti with imax t Tn .
Perform a backward iteration that starts off from Tn with payoff F(Sj , Tn) Q ( Sj K ). If ti corresponds to a settlement date, ( i.e. ti 1⁄2t Tk ti 1⁄2t for some Tk )
F(Sj L,ti)Fitr(Sj L,ti)Q(Sj K) F(Sj L,ti)Q(Sj K)
where Fitr() is the option vector immediately after the backward iteration If ti is not a settlement date, F(Sj L , ti) Fitr(Sj L , ti)
F(Sj L,ti)0
Referring to the transition at boundaries F(S0, ti 1) b0 F(S0, ti) and F(Sjmax , ti 1) bjmax F(Sjmax , ti). It is always true that bjmax 1 for Sjmax . Also, we must have b0 1 whenever the option can be exercised. Otherwise, it is generally true that b0 ert.
( 50 points )