Chapter 6. Analytical Value–at–Risk for Options and Bonds (in MATLAB/Julia)


Copyright 2011 - 2019 Jon Danielsson. This code is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This code is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. The GNU General Public License is available at: https://www.gnu.org/licenses/.


Listing 6.1/6.2: Black-Scholes function in MATLAB
Last updated 2011

%% To run this code block in Jupyter notebook:
%% delete all lines above the line with file bs.m, then run
%%file bs.m
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 6.1/6.2: Black-Scholes function in Julia
Last updated June 2018

function bs(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 .* cdf.(Normal(0,1), d1) - X * exp(-r * T) .* cdf.(Normal(0,1), d2)
    Put = X * exp(-r * T) .* cdf.(Normal(0,1),-d2) - P .* cdf.(Normal(0,1), -d1)
    Delta_Call = cdf.(Normal(0,1), d1)
    Delta_Put = Delta_Call - 1
    Gamma = pdf.(Normal(0,1), d1) ./ (P * sigma * sqrt(T))
    return Dict("Call" => Call, "Put" => Put, "Delta_Call" => Delta_Call, "Delta_Put" => Delta_Put, "Gamma" => Gamma)
end
		

Listing 6.3/6.4: Black-Scholes in MATLAB
Last updated 2011

f=bs(90,100,0.05,0.2,0.5)
		
Listing 6.3/6.4: Black-Scholes in Julia
Last updated June 2018

f = bs(90, 100, 0.05, 0.2, 0.5)