Graphically representing the properties of the option contracts

Tihomir Nikolov
14th May 2016

Five main parameters determine the price of an option contarct

  • Stock Price
  • Strike Price
  • Volatility
  • Interest Rate
  • Time

Code for calculating the Black-Scholes option price.

BS_call <- function(St,K,r,sigma,t){
    d1=(1/(sigma*sqrt(t))*(log(St/K) + (r + (sigma^2)/2)*(t)))
    d2=(1/(sigma*sqrt(t))*(log(St/K) + (r - (sigma^2)/2)*(t)))
    St*pnorm(d1) - K*exp(-r*(t))*pnorm(d2)
}

Basic Profit Plot

Plot with parameters 50 for stock and strike price, interest rate 5%, volatility 20% and time to expiration one year.

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  • By varying the five parameters we can see how the profit plot changes
  • Allows comparison between different positions (short/long), and different options (call/put)
  • Reflects the Black-Scholes pricing

Sensitivity of the Option Price

Sensitivity of the Volatolity

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  • The option price has somewhat different sensitivities towards its different parameters
  • By varying stock and strike price, interest rate, time and volatility, differencies could be discerned
  • It is divided in two groups and allows for comparisons between the call and put option

The Greek Letters

Comparison between gamma and vega for an option

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  • All greek letters are included in the app
  • Divided in two groups and allows comparisons between call and put options
  • Based on Black-Scholes formula