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I have to complete an assignment in Rstudio but I'm pretty new to it:

Compute the first order greeks (delta, vega, theta, rho, lambda, epsilon) for a plain vanilla European option using R.

I have generated the code to price the option both with Montecarlo and Binary Tree, but I have no idea how to proceed. On the internet, I found codes to generate the Greeks with the Black-Scholes model, but it's not exactly what I'm looking for.

My teacher suggested doing it with the definition of derivative.

Could someone help me?

Gaia Mancassola
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  • Here is an illustration on how to estimate delta: Compute the option price using your Monte-Carlo Code. This way you obtain `P0`. Next increase the initial stock price by `h = 0.001` (or similar) and rerun your pricing function. This way you obtain `P1`. Delta can then be obtained by `(P1 - P0) / h`. – Cettt Dec 03 '21 at 08:50
  • Thank you! No idea how to evaluate the others? – Gaia Mancassola Dec 03 '21 at 08:56
  • Not very into finance but if you want to look into derivatives, isn't Black-Scholes exactly what you need to be looking into? What about it is not what you are looking for? – koolmees Dec 03 '21 at 10:09
  • the other have the same concept behind it. But instead of shifting the stock price you shift the volatility for vega, the interest rate for rho, the time to maturity for theta. For gamme you need the second derivative wrt to the stock-price which is the first derivative of delta. – Cettt Dec 03 '21 at 11:11
  • Please provide enough code so others can better understand or reproduce the problem. – Community Dec 07 '21 at 06:42

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