1

For example: A non-dividend paying stock is currently priced at $20, and you hold a put that allows early exercise in 2 months and in 4 months. The option expires in 6 months. Volatility is 30%, and r = 5%. What is the value of this option?

I know with the payoff at time T with shout option is $Max(S_T - K, S_\tau-K, 0)$, which can be expressed as $Max(S_T-S_\tau, 0) + (S_\tau -K)$. Now we have a new strike value $S_T-S_\tau$, and we know that $S_\tau$ has to be greater than $K$. We can use the CRR binomial model with parameters: $u = e^{\sigma \sqrt{dt}} = 1.0905, d = e^{-\sigma \sqrt{dt}}=0.9170, and p = \dfrac{e^{r(dt)}-d}{u-d}=0.5024$. We can use the $Max(ST−Sτ,0)$ to find the payoff. I'm not sure if it is correct? And how do we find when we shout for the optimal payoff by algorithm(C++)? Thank you very much!

user134444
  • 13

1 Answers1

0

Time interval is 1 month. Early exercise in 2 and 4 allows to find the payoff by backward induction and comparing the discounted probability weighted Binomial price of the put option at each node backward from the 6 month time frame. Compute payoff by $Max(K-S_T,0)$ at each node during the time interval t = 4, t = 2. Compare Binomial price with the payoff and exercise accordingly. Seems like an american put option. Since you have an exercise option of 2 and 4 months, whichever yields the maximum should be the time it must be exercised.

Yours method is right and you have not specified the exercise price and here is the CRR method as described by http://en.wikipedia.org/wiki/Binomial_options_pricing_model. It has been sometime for me to have priced one like this. The site gives you pseudo code.

Good luck

Thanks

Satish Ramanathan
  • 11,984