Description

Consider a European put option on a stock that has a current spot price of $80, a volatility of 25% and pays a dividend of $5.00 on 1 October 2002. The option has a strike price of $70 and matures on 1 December 2002. The risk-free interest rate is 5% (on an actual/365 basis). What is the value of this option at 1 June 2002?

Function Specification

=oBSdd(2, "1/6/02", "1/12/02", 80, 70, 0.25, D4:F4, D5:E5, 0)

It is assumed the cell references for the zero curve and dividend schedule contain the appropriate input values.

Solution

The continuous equivalent of the flat actual/365 zero curve is calculated as follows:

S*, the spot price less the present value of the future dividends paid during the life of the option, is calculated as follows:

S* = 80 - 4.92 = 75.08

Referring to the equations for d₁ and d₂ (see model definition), if S* = 75.08, X = 70, r = 0.0488, vol = 0.25 and T = 0.5014 (183/365 days), d₁ = 0.6225 and d₂ -0.4455.

As iPC = 1 (call), N(d₁) is 0.2668 and N(d₂) is 0.3280 (see oCumNorm( ) function), the Black Scholes equation becomes:

Greeks

The following Greeks are computed using the formulas specified in oBSdd() Model Greeks:

Delta

-0.266795

Gamma

0.024729

Theta

-3.263208

Vega

17.472822

Rho

-11.232359