Black Scholes

The inputs to the Black-Scholes model are the current wrong of the underlying improver (S), the form or strike price of the alternative (K), the succession to expiration of the option in fractions of a year (t), the class of the underlying asset (cr2), and the continuously-compounded risk-free interest rate (r). In this problem, the inputs are:S = $55 ?2 = 0.0625 K =$50 r = 0.10 t = 1 After identifying the inputs, solve for dl and d2: dl = [In(S/K) + (r + 0.5*?2)(t) ] / (?2t)1/2 = [In(55/50) + {0.10 + ½(0.0625)}(1) ] / (0.0625*1)1/2 = 0.9062 d2 = dl- (?2t) 1/2 = 9062 - (0.0625*1) 1/2 = 0.6562 Find N(dl) and N(d2), the area under the conventionality mold from negative eternity to dl and negative infinity to d2, respectively. N(dl) = N(0.9062) = 0.8176 N(d2) = N(0.6562) = 0.7442 harmonise to the Black-Scholes formula, the price of a European call option (C) on a non-dividend paying common stock is: C = SN(dl) - Ke-rtN(d2) = (55)(0.8176) - (50 )e-(.10)(1) (0.7442) = $11.30 The Black-Scholes expense of the call option is $11.30. For Part 2 and 3, revel adduce to the Excel spreadsheet. The Black Scholes look ons can be computed very(prenominal) handily using EXCEL. For the mathematical formulas, just enjoyment pound (x, 2.7182818) for the natural logarithmic matter, use exp(x) for the exponential function and normsdist (x) for the meter normal distribution function. It can be slow observe that for part 2 the consequence is $8.24, and for part 3 the answer is $24.01. Hence its clear that the intrinsic value rule is wrong and that option with stock price equaling the exercise price can be quite valuable. ***END***If you fate to motor a full essay, order it on our website: BestEssayCheap.com

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