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Example 1: Down and In Caplet

This instrument provides the standard caplet payoff only if the reference interest rate is below the 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

 

6.80%

Effective Date

 

Jan 1 2003

 

 

Riskless Rate

 

6.50%

Maturity Date

 

Apr 1 2003

 

 

Volatility

 

10.0%

Face Value

 

$10,000,000

 

 

Barrier Rate

 

6.75%

Accrual Method

 

Act/365 (Act)

 

 

Strike Rate

 

6.00%

 

 

 

 

 

 

 

 

As described in Table 1, the Down & In Caplet can be valued as a combination of 2 vanilla floors and 1 digital option. 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

 

(1/4/03 1/4/02) / 365 = 1.000

 

 

 

 

Discount Factor

 

Exp(-0.065*1.0) = 0.9371

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Put Digital

 

Floorlet 1

 

Floorlet 2

 

Totals

 

 

 

 

 

 

 

 

 

Long / Short

 

Long

 

Short

 

Long

 

 

Strike Rate

 

6.75%

 

6.75%

 

6.00%

 

 

Per Unit Face Value

 

(90/365) *(6.75% - 6.00%) = 0.00184931

 

(90/365) = 0.2466

 

(90/365) = 0.2466

 

 

 

 

 

 

 

 

 

 

 

Raw Value

 

0.45297754

 

0.00197139

 

0.00017345

 

 

Per Unit Value

 

0.00083770

 

0.00048609

 

0.00004277

 

$0.00039438

 

 

 

 

 

 

 

 

 

Position Face Value

 

$10,000,000

 

$10,000,000

 

$10,000,000

 

 

Position Value

 

$8,376.98

 

$4,860.97

 

$427.69

 

$3,943.71

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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