Question

Use the Black-Scholes formula to calculate the value of a European call option on silver futures. The option matures in six months. The current nine-month futures price is $10 per oz, the strike price of the option is $8, the risk free interest rate is 12% per annum and the volatility of the futures price is 18% per annum. Use the NORM.S.DIST(x) function in Excel. Round to two decimals.

What is the delta of the call option on the futures contract from Problem #1?

Answer #1

the above is formula of Black Scholes model for call valuation , value of Spot price (S) is not given ,

for Future price , F = S* e^{r t}

=> S = 10 / e ^{0.12*0.75} = $ 9.14.

Input Data |
||

Stock Price now (S) | 9.14 | |

Exercise Price of Option (K) | 8 | |

Number of periods to Exercise in years (t) | 0.50 | |

Compounded Risk-Free Interest Rate (rf) | 12.00% | |

Standard Deviation (annualized s) | 18.00% | |

Output Data |
||

Present Value of Exercise Price (PV(K)) | 7.5341 | |

s*t^.5 | 0.1273 | |

d1 | 1.5817 | |

d2 | 1.4544 | |

Delta N(d1) Normal Cumulative Density Function | 0.9431 | |

N(d2)*PV(K) | 6.9848 | |

Value of Call |
1.6355 |

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