American Put Option Pricing

Question

I am trying to solve a question of American Put Option pricing as below.

Build a 15-period binomial model whose parameters should be calibrated to a Black-Scholes geometric Brownian motion model with: T=.25 years, S0=100, r=2%, σ=30% and a dividend yield of c=1%. Compute the fair value of an American put option with strike K=110 and maturity n=15 periods.

I built the stock and option lattice and my model is showing the price of the American put option is 10.89 but this is not the correct answer. I am wondering if anyone can assist in guide me on how to solve and find the correct American put option price? Thanks.

Answer 1

It's hard to help without knowing how you tried to solve the problem.

However, here's an idea:

• try to make the model simpler (simpler parameters) and price a simpler claim. Then look at the results. Are they correct now? If yes, then you can look at your code and figure out what might be going wrong when you change the parameters.
• If your result is incorrect regardless of what parameters you chose, then, again, price a simple option, but also work it out by hand. Work through the entire tree and compare your manual solution to your code's output (you should be outputting the entire tree). Where does it go wrong first?

Basically, just try to figure out what part of your code is causing the mistake. Note that several parts of your code may be causing the mistake, but you need to find each one, fix it, and then repeat the process until it works.

Don't let it frustrate you: that's how everybody does it. Very few write code that just works on first attempt. Debugging is part of coding. What's important though is that you understand the binomial method and how it works: you need to know that in order to be able to actually spot a mistake in your code.

The above usually works.