Delta Hedging a put option

6 次查看（过去 30 天）
Georgios Mourouzis
编辑： Voss 2022-7-3
Hello guys!! I wrote this code in order to find the cost of delta hedging a european put option and find its price. However while it runs it returns false results
function P=DeltaHedgingPut(S0,K,mu,r,T,sigma,Paths)
[NRepl,NSteps]=size(Paths);
NSteps=NSteps-1; %Τα χρονικα βηματα
Cost=zeros(NRepl,1);
dt=T/NSteps;
CashFlows=zeros(1,NSteps+1);
DiscountFactors=exp(-r*(0:1:NSteps)*dt);
for i=1:NRepl
Path=Paths(i,:);
Position=0;
Delta=blsdelta(Path(1:NSteps),K,r,T-(0:NSteps-1)*dt,sigma);
for j=1:NSteps
CashFlows(j)=(Position-Delta(j))*Paths(j);
Position=-Delta(j);
end
if Paths(NSteps+1)<K
CashFlows(NSteps+1)=-K+(1-Position)*Paths(NSteps+1);
else
CashFlows(NSteps+1)=Position*Path(NSteps+1);
end
Cost(i)=-dot(CashFlows,DiscountFactors);
end
P=mean(Cost);
end
In the command window i get this :
>> S0=37;K=40;mu=0.15;r=0.04;T=0.75;sigma=0.2;NRepl=15000;NSteps=269;
>> randn('state',0);
>> Paths=SPaths(S0,mu,sigma,T,NSteps,NRepl);
>> DeltaHedgingPut(S0, K, mu, r, T, sigma, Paths)
ans =
1.9499e+04
SPaths is used to create create different movements of thge stock of which the option is tied to
this is the code for SPaths :
function SPaths=SPaths(S0,mu,sigma,T,NSteps,NRepl)
dt=T/NSteps;
nudT=(mu-0.5*sigma^2)/dt;
sidT=sigma*sqrt(T);
Increments=nudT+sidT*randn(NRepl,NSteps);
LogPaths=cumsum([log(S0)*ones(NRepl,1),Increments],2);
SPaths=exp(LogPaths);
SPaths(:,1)=S0;
What could the mistke be ?? i cant find it anywhere??
Could it be in the Paths code? Although i doudt it !
Thanks in advance for your time and help !!
  1 个评论
dpb
dpb 2022-7-3
Format and indent the code at a minimum...
Probably very few regulars have a klew of what "delta hedging a european put option" is, what more how to calculate its cost, so with zero amplification of what is the base solution, I'd wager the chance of anybody here being able to spot a problem is minimal at best.
However, the line Position=-Delta(j);
for j=1:NSteps
CashFlows(j)=(Position-Delta(j))*Paths(j);
Position=-Delta(j);
end
looks highly suspicious to me of subsequent use being what is really intended. I have no idea what this is trying to compute; just sayin'...

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