barriers {derivmkts}

Barrier option pricing

Description

This library provides a set of barrier binary options that are used to construct prices of barrier options. The nomenclature is that

• "call" and "put" refer to claims that are exercised when the asset price is above or below the strike;

• "up" and "down" refer to claims for which the barrier is above or below the current asset price; and

• "in" and "out" refer to claims that knock in or out

For example, for standard barrier options, calldownin refers to a knock-in call for which the barrier is below the current price, while putdownout refers to a knock-out put for which the barrier is below the current asset price.

For binary barrier options, "ui", "di" "uo", and "do" refer to up-and-in, down-and-in, up-and-out, and down-and-out options.

Rebate options pay \$1 if a barrier is reached. The barrier can be reached from above ("d") or below ("d"), and the payment can occur immediately ("ur" or "dr") or at expiration ("drdeferred" and "urdeferred")

callupin(s, k, v, r, tt, d, H) = assetuicall(s, k, v, r, tt, d, H) - k*cashuicall(s, k, v, r, tt, d, H)

Usage

callupin(s, k, v, r, tt, d, H)
callupout(s, k, v, r, tt, d, H)
putupin(s, k, v, r, tt, d, H)
putupout(s, k, v, r, tt, d, H)
calldownin(s, k, v, r, tt, d, H)
calldownout(s, k, v, r, tt, d, H)
putdownin(s, k, v, r, tt, d, H)
putdownout(s, k, v, r, tt, d, H)
uicall(s, k, v, r, tt, d, H) ## same as callupin
uocall(s, k, v, r, tt, d, H) ## same as callupout
uiput(s, k, v, r, tt, d, H)  ## same as putupin
uoput(s, k, v, r, tt, d, H)  ## same as putupout
dicall(s, k, v, r, tt, d, H) ## same as calldownin
docall(s, k, v, r, tt, d, H) ## same as calldownout
diput(s, k, v, r, tt, d, H)  ## same as putdownin
doput(s, k, v, r, tt, d, H)  ## same as putdownout
cashuicall(s, k, v, r, tt, d, H)
cashuiput(s, k, v, r, tt, d, H)
cashdicall(s, k, v, r, tt, d, H)
cashdiput(s, k, v, r, tt, d, H)
assetuicall(s, k, v, r, tt, d, H)
assetuiput(s, k, v, r, tt, d, H)
assetdicall(s, k, v, r, tt, d, H)
assetdiput(s, k, v, r, tt, d, H)
cashuocall(s, k, v, r, tt, d, H)
cashuoput(s, k, v, r, tt, d, H)
cashdocall(s, k, v, r, tt, d, H)
cashdoput(s, k, v, r, tt, d, H)
assetuocall(s, k, v, r, tt, d, H)
assetuoput(s, k, v, r, tt, d, H)
assetdocall(s, k, v, r, tt, d, H)
assetdoput(s, k, v, r, tt, d, H)
dr(s, v, r, tt, d, H, perpetual)
ur(s, v, r, tt, d, H, perpetual)
drdeferred(s, v, r, tt, d, H)
urdeferred(s, v, r, tt, d, H)

Arguments

s

Stock price

k

Strike price of the option

v

Volatility of the stock, defined as the annualized standard deviation of the continuously-compounded return

r

Annual continuously-compounded risk-free interest rate

tt

Time to maturity in years

d

Dividend yield, annualized, continuously-compounded

H

Barrier

perpetual

Boolean for the case where an up or down rebate is infinitely lived. Default is FALSE.

Details

Returns a scalar or vector of option prices, depending on the inputs

Value

The pricing functions return the price of a barrier claim. If more than one argument is a vector, the recycling rule determines the handling of the inputs.

Examples

s=40; k=40; v=0.30; r=0.08; tt=0.25; d=0; H=44
callupin(s, k, v, r, tt, d, H)

## following returns the same price as previous
assetuicall(s, k, v, r, tt, d, H) - k*cashuicall(s, k, v, r, tt, d, H)

## return option prices for different strikes putupin(s, k=38:42,
#v, r, tt, d, H)