(i) Using the information from the Friday, October 26, 1996 Wall Street Journal, calculate

the implied volatility from the S&P 100 index (put only). In particular, calculate for all

strike/exercise prices between 660 and 680 for options expiring in December and January

only. Note that by design index options expire on the 3rd Friday of each month so

calculate the time to maturity accordingly (assume 365 day year). In addition, use the

risk-free rate (T-Bills) closest to expiration date of the option. Remember that the RF rate

is quoted in annualized terms.

! 2

Graph the implied volatility against the strike price on a separate graph for December and

January.

Is the volatility constant?

To solve for the implied volatility you may use trial and error by equating the theoretical

price from B-S (which you must compute) to the actual market (closing price) by trial

and error, i.e. varying , but I recommend using either the Solver or Goal Seek function

in Excel.

(ii) Use the above data to estimate delta. Create graph in excel.

(iii) Use the above data to estimate gamma. Create graph in excel.

12/16/2004 17:39 | 5164634634 SCHOOL OF BUSINESS PAGE 01 Month cailor put *pTH Tyle 4F, - Valom 3:: ssss Leslas Pic THE WALL STREET JOURNAL FRIDAY, OCTOBER 25, 1996 cl INDEX OPTIONS TRADING RANGES FOR UNDERLYING INDEXES Thursday, October 19 Net From F1 AP5 Ch. B-Medico (MEX) Top Russell 2000 (RUT) ps SteP 100 COEX SAP Midcap amus Maker Mit Hong Kong (NEC HR CHAL 1 mm m |- ||11 HEAT* ? DER RE DREASURY BILLS |||||||||||| !!!!!*!!!,! PB STRUTI33328377***8178371588308RTIST Ma EFFE PAGE 02 Black-Scholes Formulas for a Call and a Put and the Implied Volatilities 4 Option Call Inputs X.r,1,0,So Output Formula Cu = SAN(d) - Xe Ng) Put X,1,1,0, S. Po P% = SAN(-4) + Xe N(-d)) Call X,1,T,So, market call price o = "implied volatility" o that makes: market call price = SoN(D) - Xe "N(D2) SCHOOL OF BUSINESS Put X,1,1,So, market call price o = "implied volatility" o that makes: market put price = -S.N(-di) + Xe TN(-da) where OJT 5164634834 dz =d, - of and N(d)= cumulative normal distribution 12/16/2004 17:39 12/16/2004 17:39 | 5164634634 SCHOOL OF BUSINESS PAGE 01 Month cailor put *pTH Tyle 4F, - Valom 3:: ssss Leslas Pic THE WALL STREET JOURNAL FRIDAY, OCTOBER 25, 1996 cl INDEX OPTIONS TRADING RANGES FOR UNDERLYING INDEXES Thursday, October 19 Net From F1 AP5 Ch. B-Medico (MEX) Top Russell 2000 (RUT) ps SteP 100 COEX SAP Midcap amus Maker Mit Hong Kong (NEC HR CHAL 1 mm m |- ||11 HEAT* ? DER RE DREASURY BILLS |||||||||||| !!!!!*!!!,! PB STRUTI33328377***8178371588308RTIST Ma EFFE PAGE 02 Black-Scholes Formulas for a Call and a Put and the Implied Volatilities 4 Option Call Inputs X.r,1,0,So Output Formula Cu = SAN(d) - Xe Ng) Put X,1,1,0, S. Po P% = SAN(-4) + Xe N(-d)) Call X,1,T,So, market call price o = "implied volatility" o that makes: market call price = SoN(D) - Xe "N(D2) SCHOOL OF BUSINESS Put X,1,1,So, market call price o = "implied volatility" o that makes: market put price = -S.N(-di) + Xe TN(-da) where OJT 5164634834 dz =d, - of and N(d)= cumulative normal distribution 12/16/2004 17:39