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;