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oBSw( ) Example 2

Description

Consider a stock that has 1 million outstanding shares, a current spot price of $25, a volatility of 30%, and pays a dividend of $2.00 on 1 December 2002. There are 100,000 warrants on issue each entitling the holder to 10 shares in the stock. The warrants have a strike of $35 and mature on 1 June 2003, while the risk-free interest rate is 6% (on an actual/365 basis). What is the value of each warrant as at 1 August 2002?

 

 

Function Specification

=oBSw("1/8/02", "1/6/03", 25, 35, 0.3, 0.06, 1000000, 100000, 10, A1:B1, 0)

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

 

 

Solution

When calculating warrant values, the iteration procedure uses zero as the initial estimate of the warrant price. The procedure will iterate using more and more precise estimates of the warrant price until the outputted warrant value is within 15 decimal places of the inputted warrant value (see model definition).

The continuous equivalent of the actual/365 risk-free interest rate is calculated as follows:

Equation Template

Referring to the equations for d1 and d2 (see model definition), if S = 25, X = 35, r = 0.0583, vol = 0.3, ti = 0.4986 (182/365 days) and T = 0.8329 (304/365 days), d1 = -0.9148 and d2 -1.1886.

 

 

As N(d1) is 0.1801 and N(d2) is 0.1173 (see oCumNorm( ) function), the Black Scholes warrant equation becomes:

 

Equation Template

 

Since the outputted warrant value ($1.2086) is above the inputted warrant price ($0.00), the valuation is re-run with W = $1.5411. This gives a warrant price of 1.6296.

 

 

This process continues until the convergence criteria is met, which for this example occurs on the 14th iteration at a warrant price of $1.6351.

 

Equation Template

 

 

 

 

Greeks

The following Greeks are computed using a discrete approximation of the partial derivative (see oBSw() Model Greeks):

Delta

0.6243511

Gamma

-0.1858957

Theta

-4.7362376

Vega

22.17412

Rho

10.61864

 

 

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