Computational Finance: March 2015

Wednesday, March 18, 2015

C++ Coding - Black Scholes Option Pricing - Explicit Finite Difference

The example question for these solutions can be found on my website (click here).

6.1 Explicit Finite Difference For Option Pricing

In this example we are going to price a European call option with explicit finite difference.

Friday, March 13, 2015

C++ Coding - Black Scholes Option Pricing - Binomial Trees

The example question for these solutions can be found on my website (click here).

5.1 Binomial Tree For Option Pricing

The two most popular models for using binomial trees to price options are

Cox et al. (1979) (CRR for short) whose extra degree of freedom is to set $ud = 1$
thus
$√ -- √ -- rΔt u = eσ Δt, d = e−σ Δt, q = e----−-d u − d$
Rendleman and Bartter (1979) who choose: $1 q = -- 2$
and so
$(r− 12σ2)Δt+σ√Δt (r− 12σ2)Δt− σ√ Δt u = e , d = e .$

We wish to generate a stock price tree, so denote the value of the underlying asset after timestep i and upstate j by S_ij and we have that:

S = S ujdi−j ij 0

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