Matlab exercise 計財 16 陳怡鳳

Plot BLS_P % PlotBLS.m S0 = 20:1:70; X = 50; r = 0.04; sigma = 0.4; for T=2:-0.25:0 [c,p]=blsprice(S0,X,r,T,sigma); plot(S0,p); hold on; end axis([ ]); grid on Question : 自己寫的 b-s model 即使用兩個迴圈還是無法跑 (?

Output 價外 s>50 價內 s<50 價平 =s50 ？

Option price= intrinsic value + time value Intrinsic value(for put) = Max(0,X-S) Time value = The value for waiting Time value may be negative For deep in the money only. More possible for put than call.

Plot the variation of theta with stock price for a call x=50; r=0.05; t=0.5; sig=0.2; div=0; s=30:120; [call_theta,put_theta]=blstheta(s,x,r,t,sig,div); figure plot(s,call_theta,'-') title('theta vs. s') xlabel('s') ylabel('theta') legend('theta of call')

Plot the variation of gamma with stock price for a call x=50; r=0.05; t=0.5; sig=0.2; div=0; s=30:120; gamma=blsgamma(s,x,r,t,sig,div); figure plot(s,gamma,'-') title('gamma vs. s') xlabel('s') ylabel('gamma') legend('gamma')

Plot the variation of vega with stock price for a call x=50; r=0.05; t=0.5; sig=0.2; div=0; s=30:120; vega=blsvega(s,x,r,t,sig,div); figure plot(s,vega,'-') title('vega vs. s') xlabel('s') ylabel('vega') legend('vega')

Plot the patterns for variation of delta with time to maturity for a call option x=50; r=0.05; t=0.5:20; sig=0.2; div=0; s1=30; [call_delta1,put_delta]=blsdelta(s1,x,r,t,sig,div); s2=50; [call_delta2,put_delta]=blsdelta(s2,x,r,t,sig,div); s3=70; [call_delta3,put_delta]=blsdelta(s3,x,r,t,sig,div); plot(t,call_delta1,'-',t,call_delta2,'-',t,call_delta3,'-') title('Delta vs. t') xlabel('time to maturity ') ylabel('Delta of call') legend('out the money','at the mpney','in the money')

For interest _ call and put delta comparison x=50; r=0.05; t=0.5; sig=0.2; div=0; s=30:80; [call_delta,put_delta]=blsdelta(s,x,r,t,sig,div); change=call_delta-put_delta; figure plot(s,call_delta,'-',s,put_delta,'-',s,change,'-') title('Delta vs. s') xlabel('s') ylabel('Delta') legend('call Delta','put delta','call delta minus put delta') axis([ ]);