The module includes functions to measure the static risks/sensitivities of financial contracts. Static, in this sense, means "What happens when we go from state 1 to state 2?". Of course, the rate at which the change occurs is of great importance and must also be evaluated.

TermStructureRisk is defined as the profit or loss on a position - an actual asset or liability holding - stemming from a shift in the term structure from state 1 to state 2. The first term structure represents the state before any change in the term structure has occured, and the second term structure represents the state after the change. TermStructureRisk is also available in a general version that takes a cash flow and two term structure functions - one for state 1 and one for state 2 - as input.

The function Duration can be used to calculate the average time until the cash flow is received. This is the Macaulay method. Duration can also be used to calculate the term structure risk on cash flows that are not dependent on the yield level. This is the ModifiedMacaulay method. The duration is based on first partial derivatives and is therefore not always an accurate method for measuring term structure risk, also because it implicitly assumes that term structures are flat .

The function TermStructureRisk is generally a more correct way of measuring static term structure risk than Duration. The function TermStructureRisk does not put any restrictions on the form of the term structures - except that there must be a one-to-one correspondence between x-values and y-values for the needed range of x-values.

The D function is used to calculate the first and second order partial derivatives of some option pricing functions, and it is shown how to easily calculate these partial derivatives for all option pricing models of Derivatives Expert.

Information on the Elasticity function is provided. Elasticity is used to calculate an option's price elasticity. Price elasticity is defined as the relative change in the option's price, caused by a relative change in one of the function's variables, e.g. the spot price of the underlying security.

Context

 Functions are included in the Bonds module to calculate the term structure risk and duration on the following instrument types: Annuity, Bullet, Consol, Serial and Zero.

The modules: MortgageBackedObligations, Forwards, Floaters and Swaps include functions to calculate the term structure risk on the following instrument types: PassThrough, ForwardRateAgreement, MoneyMarketForward, ForeignExchangeForward, Float, InterestRateSwap and PlainCurrencySwap.

The BlackScholes module (Black & Scholes, 1973, option pricing formulas) provides all first and second order partial derivatives and elasticities on European call and put options on non-dividend paying stock. Refer to the Options and Option Graphics modules

The Black76 module (Black, 1976, option pricing formulas) provides all first and second order partial derivatives and elasticities on European call and put options on commodities. The exact nature of the underlying commodity varies and may be anything from a precious metal such as gold or silver to agricultural products.

The GarmanKohlhagen module (Garman & Kohlhagen, 1983, option pricing formulas) provides all first and second order partial derivatives and elasticities on European call and put options on foreign exchange.

Contents

7.1 Introduction

Summary -- Context -- This Opens the Package

7.2 General Functions/Components

Duration -- TermStructureRisk -- SubtractPresentValues
Elasticity -- +D (an extended Mathematica symbol)