schwartz97priceoption: Schwartz two-factor Model: European Option Prices

In schwartz97: A package on the Schwartz two-factor commodity model

Description

Compute arbitrage-free prices of European call and put options on commodity futures contracts.

Usage

## S4 method for signature 'ANY,ANY,ANY,ANY,numeric'
priceoption(type = c("call", "put"), time = 0.5, Time = 1, K = 40,
            g0 = 50, sigmaS = 0.3, kappa = 1, sigmaE = 0.5,
            rho = 0.75, r = 0.03)

## S4 method for signature 'ANY,ANY,ANY,ANY,schwartz2f'
priceoption(type = c("call", "put"),
            time = 0.5, Time = 1, K = 40,
            g0, r = 0.03, lambda = 0, alphaT = NULL)

## S4 method for signature 'ANY,ANY,ANY,ANY,schwartz2f.fit'
priceoption(type = c("call", "put"),
            time = 0.5, Time = 1, K = 40, g0)

Arguments

type	Either a European "call" or a "put" option on a futures contract.
time	Exercise time of the option.
Time	Maturity date of the underlying futures (see Details).
K	Strike price.
g0	The current futures price or an object inheriting from class schwartz2f.
sigmaS	Diffusion parameter of the spot price-process.
kappa	Speed of mean-reversion of the convenience-yield process.
sigmaE	Diffusion parameter of the convenience-yield process.
rho	Correlation coefficient between the Brownian motion driving the spot-price and the convenience-yield process.
r	Instantaneous risk-free interest rate.
lambda	Market price of convenience yield risk (see Details).
alphaT	Mean-level of the convenience yield process with respect to the equivalent martingale measure (see Details).

Details

The price of an option on the spot commodity is obtained by setting time == Time. This is because of the convergence of the futures price towards the spot price at maturity. In general the option expires before the futures contract (time < Time).

If g0 is either of class schwartz2f or class schwartz2f.fit the futures price g0 is computed first and then plugged into the pricing function with signature ANY,ANY,ANY,ANY,numeric.

The model and its parameters are described in the Details section of the schwartz2f-class documentation and in the package vignette Technical Document.

Value

A numeric containing the option prices.

Note

Since the two-factor model assumes a constant interest rate, futures and forwards always have the same value and therefore also any derivative of futures or forwards.

Author(s)

Philipp Erb, David Luethi, Juri Hinz

References

The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging by Eduardo S. Schwartz
Journal of Finance 52, 1997, 923-973

Pricing of Options on Commodity Futures with Stochastic Term Structures of Convenience Yields and Interest Rates by Kristian R. Miltersen and Eduardo S. Schwartz
Journal of Financial and Quantitative Analysis 33, 1998, 33-59

Valuation of Commodity Futures and Options under Stochastic Convenience Yields, Interest Rates, and Jump Diffusions in the Spot by Jimmy E. Hilliard and Jorge Reis
Journal of Financial and Quantitative Analysis 33, 1998, 61-86

See Also

pricefutures to price futures, d/p/q/rfutures to work with futures, schwartz2f-constructor, fit.schwartz2f for parameter estimation, futures-data.

Examples

## The option expires in 0.5 years and the futures contract in 1 year.
priceoption(type = "call", time = 0.5, Time = 1, K = 40, g0 = 50)

## The price of a European put option on the spot which expires in 2.5
## years.
priceoption(type = "put", time = 2.5, Time = 2.5, K = 900, lambda = 0.02,
            g0 = schwartz2f(s0 = 1000))

schwartz97 documentation built on May 2, 2019, 5:48 p.m.