Previous Topic

Next Topic

Example 3: Down & Out / Up & Out Caplet

This instrument provides the standard caplet payoff only if the reference interest rate falls between the upper and lower barrier rate on the maturity date. The required deal details are set out in the following table.

Deal Details

 

 

 

 

 

 

 

 

Value Date

 

Apr 1 2002

 

 

Forward Rate

 

6.75%

Effective Date

 

Jan 1 2003

 

 

Riskless Rate

 

6.50%

Maturity Date

 

Jul 1 2003

 

 

Volatility

 

10%

Face Value

 

$10,000,000

 

 

Upper Barrier Rate

 

8.00%

Accrual Method

 

Act/365 (Act)

 

 

Lower Barrier Rate

 

7.00%

 

 

 

 

 

Strike Rate

 

6.50%

As described in Table 4, the Down & Out / Up & Out Caplet can be valued as a combination of 2 vanilla caps and 2 digital options. The following table presents the intermediate valuation results for each of the component building blocks.

Component Valuation

 

 

 

 

 

 

Common Parameters

 

 

 

 

 

Time to Maturity

(1/1/03 1/4/02) / 365 = 0.7534

 

 

Time to Payment

(1/7/03 1/4/02) / 365 = 1.2493

 

 

Discount Factor

Exp(-0.065*1.2493) = 0.9220

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Call Digital 1

Caplet 1

Call Digital 2

Caplet 2

Totals

 

 

 

 

 

 

Long / Short

Long

Long

Short

Short

 

Strike Rate

7.00%

7.00%

8.00%

8.00%

 

Per Unit Face Value

(181/365) *(7.00% - 6.50%) = 0.00247945

(181/365) = 0.495890

(181/365) *(8.00% - 6.50%) = 0.00743836

(181/365) = 0.495890

 

 

 

 

 

 

 

Raw Value

0.29679661

0.00123150

0.02093778

0.00005590

 

Per Unit Value

0.00073589

0.00061069

0.00015574

0.00002772

$0.00116312

 

 

 

 

 

 

Position Face Value

$10,000,000

$10,000,000

$10,000,000

$10,000,000

 

Position Value

$7,358.93

$6,106.89

$1,557.43

$277.18

$11,631.22

 

 

 

 

 

 

 

 

 

 

 

 

Return to www.derivativepricing.com website

Copyright 2013 Hedgebook Ltd.