To apply Monte-Carlo simulations and calculate price of American style options.
Use of Monte-Carlo Simulations
In order to calculate Option prices, we need to calculate the expected price at Expiry date of the underlying asset. One of the ways to do this is by running Monte-Carlo simulations as I had pointed out in my previous blog.
Calculate Expected Payoffs
Once we have expected prices calculated, next step is to calculate the Option payoffs for those prices.
Present Value of expected Payoffs
Now, we have the expected Options payoffs; so the next step is to calculate their Present Value using the discount factor dependent on risk-free rate and time to expiry (in years).
We use the above discount factor to calculate the present-value of option payoffs returns through the Monte-Carlo simulations.
Ct = PV(E[max(0,PriceAtExpiry−Strike)])
Pt = PV(E[max(0,Strike−PriceAtExpiry)])
Below code performs this exact calculation and returns the American Call and Put Option prices
Calculate Present Value of Expected Option Payoffs
Running for an extremely volatile asset - TSLA
We have everything setup, so lets start these simulations and calculations on TSLA stock to calculate prices for Call and Put option expiring Sept 7th, 2018 (i.e. 1 month from now) and with Strike price of $370.
The output we receive is Call Option priced at $11.162 and Put option prices at $25.102. Given the current Spot price is $355.49 (as of EOD Aug 10th), this price somewhat looks fine; but let's confirm it with other sites.
Output for TSLA Strike 370 expiring September 7th, 2018
As we can see from above Yahoo screenshots, our calculated option prices are pretty close to the ones found in Yahoo. I wonder if the recent news of Tesla going private adds additional volatility to the stock; causing this minor increase in both Call and Put option prices. What do you think?
I am a passionate, driven polyglot programmer and architect with a knack of solving complex problems in quick and efficient way. Along with programming, software development, financial products, and management expertise, I also bring skills in statistical modeling, empowering me to work on challenging projects that require combination of software development and quantitative analysis.