BLACK-SCHOLES MODEL An analyst is interested in using the Black-Scholes model to value call options

QUESTION

BLACK-SCHOLES MODEL An analyst is interested in using the Black-Scholes model to value call options on the stock of Ledbetter Inc. The analyst has accumulated the following information:The price of the stock is $33.The strike price is $33.The option matures in 6 months (t = 0.50).The standard deviation of the stocks returns is 0.30, and the variance is 0.09.The risk-free rate is 10%.Given that information, the analyst is able to calculate some other necessary components of the Black-Scholes model_d1= 0.34177d2= 0.12964N(d1) = 0.63369N(d2) = 0.55155N(d1) and N(d2) represent areas under a standard normal distribution function. Using the Black-Scholes model, what is the value of the call option?
Black Scholes Model(BSM) equation is given by, Value of Call option = Price of stock*N(d1) (Exercise Price*N(d2)) / e^rt where,e^rt = e^0.10*0.50 =e^0.05 =1.05127 (as per the value in the table for

e^x) Therefore,Value of call option = 33*0.63369 -(33*0.55155)/1.05127 =20.91177-18.20115/1.05127 =20.91177-17.313487 =3.5982 (Ans)

ANSWER:

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