BondOption

(OptionType, BondPriceType, ModelStatistic, Principal, StrikePrice, TimeExpire, TimeMaturity, Volatility, CouponRate, Frequency, TermStructure, MarketPrice, TimeFormat, RateType)

Argument

Description

OptionType

Alphanumeric value indicating the type of option:

•Call = 1 or "c" (case insensitive)

•Put = 2 or "p" (case insensitive)

BondPriceType

Alphanumeric value indicating the type of bond price:

•Quoted Price = 0 or "q" (case insensitive)

•Cash Price = 1 or "c" (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

•StrikeSensitivity = 11

•Implied Strike = 13

Principal

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

StrikePrice

The price at which the asset can be purchased if the option is a call or sold if the option is a put. Must be > 0.

TimeExpire

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

TimeMaturity

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

Volatility

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

CouponRate

The annual coupon 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

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.

Quoted Bond Option Valuation

Calculate the Quoted Theoretical and Gamma values of a Bond 3 month Call Option whose principal two years from maturity is $100, the strike price is $98, the coupon rate is 5.5% per annum with semi annual coupon frequency. The volatility is 25%. The coupon or term structure is as follows: 0 to 1.0 years at 2.5%, 1.0 to 2.0 years at 3.0%, 2.0 years and after at 3.5%. This means that Principal = $100, Strike = $98, CouponRate = 5.5%, TimeExpiration = 0.25, TimeMaturity = 2, Volatility = 25%, and CouponFrequency = Semi-Annual. All interest rates are considered continuous and the following term structure is in place:

So,

Input

Output

Variable

Value

Function

Name

Value

OptionType

Call

1

Theoretical:

5.071338

Bond Price Type

Quoted Price

2

Delta:

-0.017488

Principal

100

3

Gamma:

0.000386

Strike

98

4

Theta:

0.005112

Time to Expiration

0.25

5

Implied Vol:

2.277873

Time to Maturity

2.00

6

Vega:

0.000000

Coupon Rate

5.5

7

Rho:

1.671079

Frequency

Semi-Annually

9

Lambda:

20.197888

Market Price

6.00

11

Strike Sens:

-0.993459

Time Format

Years

13

Implied Strike:

97.065224

Term Structure

Coupon

Rate

0.0

2.50%

1.0

3.00%

2.0

3.50%

Futures

Bonds

Cap Floor Options

Swaption