Problem Set 9 helpful hints – part 1 of 2

During last Thursday’s class meeting of Finance 4335, we completed our coverage of the Cox-Ross-Rubinstein (CRR) model (as outlined on pages 9-11 of the Part 2 option pricing lecture note and pages 11-13 of the Teaching the Economics and Convergence of the Binomial and Black-Scholes Option Pricing Formulas assigned reading).  This coming Tuesday’s class meeting will be devoted to 1) showing how CRR model probabilities and prices converge to BSM (Black-Scholes-Merton) model probabilities and prices as the number of timesteps becomes arbitrarily large, and 2) showing how the BSM model can be applied to the pricing and management of credit risk.

In the meantime, it’s not too early to begin working on Problem Set 9, Problem 1.  Here are some helpful hints to consider:

  • Since the call option described in Problem 1, Part A is initially out-of-the-money (i.e., since S = $18 and K = $20), there will be terminal nodes at which the call option expires in-the-money and others at which it expires out-of-the-money.  By solving the b = \ln (K/S{d^n})/\ln (u/d) equation and rounding to the nearest integer greater than b (referred to in the above-referenced sources as the parameter “a“), this indicates the minimum number of up moves required such that this call option expires inthemoney.  Once you have this information, you can consider only those terminal nodes at which the call option expires in-the-money (which are nodes a through n) and calculate the call option price by applying the CRR call option pricing equation:  C = {e^{ - rT}}\left[ {\sum\limits_{j = a}^n {\frac{{n!}}{{j!\left( {n - j} \right)!}}{q^j}{{\left( {1 - q} \right)}^{n - j}}\left( {{u^j}{d^{n - j}}S - K} \right)} } \right]
  • Part B: Apply the put-call parity equation (C+Ke^{-rT} =P+S) to solve for the put option price.

Leave a Reply

Your email address will not be published. Required fields are marked *

%d bloggers like this: