CapFloor

(CapFloorType, ModelStatistic, Principal, Tenor, TimeMaturity, Volatility, ForwardRate, Frequency, TermStructure, YearBasis, MarketPrice, TimeFormat, RateType)

Argument

Description

CapFloorType

Alphanumeric value indicating the type of option:

•Cap = 1 or "c" (case insensitive)

•Floor = 2 or "f" (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.

Tenor

Time expressed in either Days or Years (depending on the TimeFormat value) until the maturity of the underlying contract. 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.

ForwardRate

The forward 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 the bond.

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

YearBasis

Optional. Numeric value indicating the format for calculating the payments. If omitted, Actual365 is used as the default. Specified as either:

Actual365 = 0

Actual360 = 1

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.

Cap Option Valuation:

Calculate all of the functions for a 3-year Cap Option whose principal five years from maturity is $1000, the forward rate is 6.0% 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 2.0%, 1.0 to 2.0 years at 2.5%, 2.0 years and after at 3.0%. This means that Principal = $1000, ForwardRate = 6.0%, Tenor = 3, TimeMaturity = 5, 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

Cap-Floor Type

Cap

1

Theoretical:

1.99529

Principal

1000

2

Delta (DV01):

0.03092

Tenor

3

3

Gamma:

0.03092

Time to Maturity

5

4

Theta:

-0.00154

Volatility

20%

5

Implied Vol:

0.20012

Forward Rate

6.00%

6

Vega:

0.39069

Frequency

Semi-Annually

7

Rho (Forward Rate):

-0.01270

Year Basis

Actual365

9

Lambda:

18.14082

Market Price

2.00

Time Format

Years

Term Structure

Coupon

Rate

0.0

2.50%

1.0

2.50%

2.0

3.00%

Futures

Bonds

Bond Options

Swaption