asiangeomavg {derivmkts} R Documentation

## Geometric average asian options

### Description

Pricing functions for European Asian options based on geometric averages. geomavgpricecall, geomavgpriceput, geomavgstrikecall and geomavgstrikeput compute analytical prices of geometric Asian options using the modified Black-Scholes formula.

### Usage

geomavgprice(s, k, v, r, tt, d, m, cont=FALSE)
geomavgpricecall(s, k, v, r, tt, d, m, cont=FALSE)
geomavgpriceput(s, k, v, r, tt, d, m, cont=FALSE)
geomavgstrike(s, km, v, r, tt, d, m, cont=FALSE)
geomavgstrikecall(s, km, v, r, tt, d, m, cont=FALSE)
geomavgstrikeput(s, km, v, r, tt, d, m, cont=FALSE)


### Arguments

 s Price of underlying asset k Strike price of the option. In the case of average strike options, k/s is the multiplier for the average v Volatility of the underlygin asset price, 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 m Number of prices in the average calculation cont Boolean which when TRUE denotes continuous averaging km The strike mutiplier, relative to the initial stock price, for an average price payoff. If the initial stock price is s = 120 and km = 115, the payoff for an average strike call is Payoff = max(ST - km/s*SAvg, 0) .

### Value

Option prices as a vector

Other Asian: arithasianmc(), arithavgpricecv(), geomasianmc()
s=40; k=40; v=0.30; r=0.08; tt=0.25; d=0; m=3;