在MATLAB中使用BS模型计算期权希腊值

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1. function [DeltaCall, DeltaPut, Gamma, Vega] = FormulaBSGreeks( S, K, r, tau, sigma, yield)
   
2. % Evaluation of the greeks (delta, gamma, vega) for call and put options
   
3. % under the Black-Scholes model.
   
4. %
   
5. % Input: S: Actual price of the underlying asset (can be a vector);
   
6. %        K: Strike price;
   
7. %        r: (continuous) short-time interest rate for the period;
   
8. %        tau: time to maturity;
   
9. %        sigma: volatility in the B-S model;
   
10. %        yield: continuous dividend rate.
    
11. %
    
12. % Output: DeltaCall: value of the delta for the European call option;
    
13. %         DeltaPut : value of the delta for the European put option;
    
14. %         Gamma    : value of the gamma for the European call option
    
15. %                   (same value for put option);
    
16. %         vega     : value of the vega for the European call option
    
17. %                   (same value for put option).
    
18. %
    
19. % N.B.: The time and rate must be on the same scale as the one used for
    
20. %       estimating sigma. For example, if sigma was estimated with daily
    
21. %       prices, then tau should be in days, and r should be the interest
    
22. %       rate for 1 day.
    
23. if nargin < 6
    
24.     yield =0;
    
25. end
    
26. 
    
27. s = S.*exp( -yield.* tau );
    
28. d1 = ( log( s./ K )+ r.* tau + (sigma.^2).* tau / 2 )./ ( sigma.* sqrt( tau ) );
    
29. 
    
30. z = normpdf(d1);
    
31. 
    
32. DeltaCall = exp( -yield.* tau ).* normcdf(d1);
    
33. DeltaPut  = DeltaCall - exp( -yield.* tau ); % By put-call parity
    
34. 
    
35. Vega = s.*z.* sqrt( tau );
    
36. 
    
37. Gamma = exp( -yield.* tau ).*( z./s)./(sigma.*sqrt(tau));

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关键词：MATLAB matla atlab Lab Atl 模型 希腊

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