Swaption

(SwapType, ModelStatistic, Principal, SwapTenor, TimeMaturity, Volatility, SwapRate, Frequency, TermStructure, MarketPrice, TimeFormat, RateType)

Argument

Description

SwapType

Alphanumeric value indicating the type of option:

•Payer = 0 or "p" (case insensitive)

•Receiver = 1 or "r" (case insensitive)

ModelStatistic

Numeric value indicating the type of function required for the return value:

•Theoretical = 1

•Delta = 2

•Gamma = 3

•Theta = 4

•ImpliedVol = 5

•Vega = 6

•Rho = 7

•Lambda = 9

Principal

The face value of the bond asset. Must be > 0.

SwapTenor

Time expressed in either Days or Years (depending on the TimeFormat value) until the maturity of the underlying swap. Must be > 0.

TimeMaturity

Time expressed in either Days or Years (depending on the TimeFormat value) until the maturity. Must be > 0.

Volatility

Annualized volatility of the underlying security. Must be > 0.

SwapRate

The swap rate expressed as a percentage of the principal. This rate is interpreted as a continuously compounded rate unless otherwise specified in the RateType argument. Must be > 0.

Frequency

Alphanumeric value indicating the coupon payment frequency when evaluation of the Swaption.

TermStructure

A two-dimensional array or range of coupon maturity and interest rate pairs where the first column is the maturity and the second is the rate. The rates are interpreted as a continuously compounded rate unless otherwise specified in the RateType argument. All rates must be > 0.

As an example:

Term Structure

Coupon Rate

0.0    0.02

0.5    0.03

1.0    0.04

1.5    0.05

2.0    0.06

2.5    0.07

MarketPrice

Optional. The selling price of the option in the marketplace. This input is required when implied volatility and strike are calculated. Price must be > 0.

TimeFormat

Optional. Alphanumeric value indicating the format of the time arguments (i.e. TimeExpire, TimeExDiv, DivFrequency). If omitted, Days are used as the default. Specified as either:

Days = 0 or "D" (case insensitive)

Years = 1 or "Y" (case insensitive)

RateType

Optional. Alphanumeric value indicating the type of RateType used for both the CouponRate ad Term Structure Rate when evaluating the bond. This value is converted to Continuously Compounded for the calculations. If omitted, a continuously compounded rate is used.

Payer Swaption Valuation:

Calculate the Theoretical and Gamma values of a 1½-year Payer Swaption whose principal three years from maturity is $1000, the swap rate is 4.25% per annum with semi annual coupon frequency. The volatility is 20%. The coupon or term structure is as follows: 0 to 1.0 years at 2.25%, 1.0 to 2.0 years at 2.5%, 2.0 years and after at 3.0%. This means that Principal = $1000, SwapRate = 4.25%, SwapTenor = 1.5, TimeMaturity = 3, Volatility = 20%, and Frequency = Semi-Annual. All interest rates are considered continuous and the following term structure is in place:

So,

Input

Output

Variable

Value

Function

Name

Value

Swapation Type

Payer

1

Theoretical:

1.40591

Principal

1000

2

Delta (DV01):

0.02766

Swap Tenor

1.5

3

Gamma:

0.03553

Time to Maturity

3

4

Theta:

-0.00171

Volatility

20%

5

Implied Vol:

0.20465

Swap Rate

4.25%

6

Vega:

0.20007

Frequency

Semi-Annually

7

Rho (Forward Rate):

-0.01645

Market Price

1.50

9

Lambda:

24.06016

Time Format

Years

Term Structure

Coupon

Rate

0.0

2.50%

1.0

2.50%

2.0

3.00%

Futures

Bonds

Bond Options

Cap Floor Options