Black-Scholes on 17bII+ using Taylor series VERY ACCURATE! « Next Oldest | Next Newest »

 ▼ Bob Wang Member Posts: 90 Threads: 22 Joined: Jun 2005 01-13-2005, 07:47 PM Special Thanks to Tizedes Csaba for pointing me to the Taylor series approximation for the normal cumulative distribution. This implementation of Black-Scholes only works in the region where d1 and d2 are less than 3 in absolute value. If either d1 or d2 is greater than 3, 0 is returned for CALLV. Calculation time is well over a minute, but accuracy is basically to the last displayed decimal place! Note that the newer 17bII+ ROM has changed order of precedence, i.e. (-1^N) works on the older version, but has to be explicitly written as ((-1)^N) for the newer version. On a brighter note, the newer ROM is almost an order of magnitude faster at displaying equations, and opening the editing function. Also, replace * with multiply, and / with divide. Replace SIGMA with the sum operator found under the second screen of MORE Alpha characters. I apologize for the inconvenience, but I can't seem to get these characters to paste correctly. Bob Wang ```PS=52 PE=45 Rf%=.5 T=6 S=.2054 Exact Call = 14.218722263 Formula = 14.2187222629 Exact Put = 5.88877127263 Formula = 5.8887712726 Taylor Series Approximation HP 17BII+: Not using L() and G() Execution Time > 1 minute Character Count = 464 BLK.SCHLS.TAYLOR: 0*(PS+PE+RF%+T+S) +IF(S(CALLV): IF((LN(PS/PE)+(RF%/100+S^2/2)*T)/S/SQRT(T)>3:0: PS*ABS(IF((LN(PS/PE)+(RF%/100+S^2/2)*T)/S/SQRT(T)<0:-.5:.5) +SIGMA(N:0:25:1:((-1)^N) *(((LN(PS/PE)+(RF%/100+S^2/2)*T)/S/SQRT(T))^(2*N+1)) /FACT(N)/2^N/(2*N+1)) /SQRT(2*PI)) -PE*EXP(-RF%*T/100)*ABS( IF((LN(PS/PE)+(RF%/100-S^2/2)*T)/S/SQRT(T)<0:-.5:.5) +SIGMA(N:0:25:1:((-1)^N) *(((LN(PS/PE)+(RF%/100-S^2/2)*T)/S/SQRT(T))^(2*N+1)) /FACT(N)/2^N/(2*N+1)) /SQRT(2*PI)))-CALLV: -PS+PE*EXP(-RF%*T/100)+CALLV-PUTV) ```

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