R and Matlab Chapter 6. Analytical Value-at-Risk for Options and Bonds

Chapter 6. Analytical Value-at-Risk for Options and Bonds

R and Matlab

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Listing 6.1/6.2
Black-Scholes function in R
bs = function(X, P, r, sigma, T){
	d1 = (log(P/X) + (r + 0.5*sigma^2)*(T))/(sigma*sqrt(T))
	d2 = d1 - sigma*sqrt(T)
	Call = P*pnorm(d1,mean=0,sd=1)-X*exp(-r*(T))*pnorm(d2,mean=0,sd=1)
	Put = X*exp(-r*(T))*pnorm(-d2,mean=0,sd=1)-P*pnorm(-d1,mean=0,sd=1)
	Delta.Call = pnorm(d1, mean = 0, sd = 1) 
	Delta.Put = Delta.Call - 1
	Gamma = dnorm(d1, mean = 0, sd = 1)/(P*sigma*sqrt(T))
	return(list(Call=Call,Put=Put,Delta.Call=Delta.Call,Delta.Put=Delta.Put,Gamma=Gamma))
}
Listing 6.1/6.2
% Black-Scholes function in MATLAB
function  res = bs(K,P,r,sigma,T)
	d1 = (log(P./K)+(r+(sigma^2)/2)*T)./(sigma*sqrt(T));
	d2 = d1 - sigma*sqrt(T);
	res.Call = P.*normcdf(d1,0,1)-K.*exp(-r*T).*normcdf(d2,0,1);
	res.Put = K.*exp(-r*T).*normcdf(-d2,0,1)-P.*normcdf(-d1,0,1);
	res.Delta.Call = normcdf(d1,0,1);
	res.Delta.Put = res.Delta.Call -1;
	res.Gamma = normpdf(d1,0,1)./(P*sigma*sqrt(T));
end
Listing 6.3/6.4
Black-Scholes in R
f = bs(X = 90, P = 100, r = 0.05, sigma = 0.2, T = 0.5)
print(f)
Listing 6.3/6.4
% Black-Scholes in MATLAB
f=bs(90,100,0.05,0.2,0.5)
Financial Risk Forecasting
Market risk forecasting with R, Julia, Python and Matlab. Code, lecture slides, implementation notes, seminar assignments and questions.
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