Pricing of foreign exchange options under the Heston stochastic volatility model and CIR interest rates

2013 ◽  
Vol 13 (6) ◽  
pp. 955-966 ◽  
Author(s):  
REHEZ AHLIP ◽  
MAREK RUTKOWSKI
Keyword(s):  
Interest Rates ◽  
Stochastic Volatility ◽  
Foreign Exchange ◽  
Stochastic Volatility Model ◽  
Volatility Model ◽  
Exchange Options

FOREIGN EXCHANGE OPTIONS UNDER STOCHASTIC VOLATILITY AND STOCHASTIC INTEREST RATES

2008 ◽  
Vol 11 (03) ◽  
pp. 277-294 ◽  
Author(s):  
REHEZ AHLIP
Keyword(s):  
Exchange Rate ◽  
Interest Rates ◽  
Stochastic Volatility ◽  
Foreign Exchange ◽  
Stochastic Volatility Model ◽  
Stochastic Interest Rates ◽  
Volatility Model ◽  
Stochastic Interest ◽  
The Exchange Rate ◽  
Inversion Techniques

In this paper, we present a stochastic volatility model with stochastic interest rates in a Foreign Exchange (FX) setting. The instantaneous volatility follows a mean-reverting Ornstein–Uhlenbeck process and is correlated with the exchange rate. The domestic and foreign interest rates are modeled by mean-reverting Ornstein–Uhlenbeck processes. The main result is an analytic formula for the price of a European call on the exchange rate. It is derived using martingale methods in arbitrage pricing of contingent claims and Fourier inversion techniques.

A CLOSED-FORM PRICING FORMULA FOR EUROPEAN EXCHANGE OPTIONS WITH STOCHASTIC VOLATILITY

2021 ◽  
pp. 1-10
Author(s):  
Puneet Pasricha ◽  
Anubha Goel
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Closed Form Solution ◽  
Form Solution ◽  
Stochastic Volatility Model ◽  
Strike Price ◽  
Volatility Model ◽  
Exchange Options ◽  
Pricing Formula ◽  
Exchange Option

This article derives a closed-form pricing formula for the European exchange option in a stochastic volatility framework. Firstly, with the Feynman–Kac theorem's application, we obtain a relation between the price of the European exchange option and a European vanilla call option with unit strike price under a doubly stochastic volatility model. Then, we obtain the closed-form solution for the vanilla option using the characteristic function. A key distinguishing feature of the proposed simplified approach is that it does not require a change of numeraire in contrast with the usual methods to price exchange options. Finally, through numerical experiments, the accuracy of the newly derived formula is verified by comparing with the results obtained using Monte Carlo simulations.

scholarly journals South Africa’s economic response to monetary policy uncertainty

2017 ◽  
Vol 44 (2) ◽  
pp. 282-293 ◽  
Author(s):  
Mehmet Balcilar ◽  
Rangan Gupta ◽  
Charl Jooste
Keyword(s):  
Monetary Policy ◽  
Interest Rates ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Economic Consequences ◽  
Policy Uncertainty ◽  
Dsge Model ◽  
Content Type ◽  
Volatility Model ◽  
Central Bankers

Purpose The purpose of this paper is to study the evolution of monetary policy uncertainty and its impact on the South African economy. Design/methodology/approach The authors use a sign restricted SVAR with an endogenous feedback of stochastic volatility to evaluate the sign and size of uncertainty shocks. The authors use a nonlinear DSGE model to gain deeper insights about the transmission mechanism of monetary policy uncertainty. Findings The authors show that monetary policy volatility is high and constant. Both inflation and interest rates decline in response to uncertainty. Output rebounds quickly after a contemporaneous decrease. The DSGE model shows that the size of the uncertainty shock matters – high uncertainty can lead to a severe contraction in output, inflation and interest rates. Research limitations/implications The authors model only a few variables in the SVAR – thus missing perhaps other possible channels of shock transmission. Practical implications There is a lesson for monetary policy: monetary policy uncertainty, in isolation from general macroeconomic uncertainty, often creates unintended adverse consequences and can perpetuate a weak economic environment. The tasks of central bankers are incredibly difficult. Their models project output and inflation with relatively large uncertainty based on many shocks emanating from various sources. It matters how central bankers react to these expectations and how they communicate the underlying risks associated with setting interest rates. Originality/value This is the first study that looks into monetary policy uncertainty into South Africa using a stochastic volatility model and a nonlinear DSGE model. The results should be very useful for the Central Bank as it highlights how uncertainty, that they create, can have adverse economic consequences.

A STOCHASTIC VOLATILITY MODEL FOR RISK-REVERSALS IN FOREIGN EXCHANGE

2009 ◽  
Vol 12 (06) ◽  
pp. 877-899 ◽  
Author(s):  
CLAUDIO ALBANESE ◽  
ALEKSANDAR MIJATOVIĆ
Keyword(s):  
Stochastic Volatility ◽  
Foreign Exchange ◽  
Continuous Time ◽  
Efficient Algorithms ◽  
Stochastic Volatility Model ◽  
Foreign Exchange Markets ◽  
Local Volatility ◽  
Volatility Model ◽  
Exchange Markets

It is a widely recognized fact that risk-reversals play a central role in the pricing of derivatives in foreign exchange markets. It is also known that the values of risk-reversals vary stochastically with time. In this paper we introduce a stochastic volatility model with jumps and local volatility, defined on a continuous time lattice, which provides a way of modeling this kind of risk using numerically stable and relatively efficient algorithms.

Forwards, Futures, and More Option Pricing

2017 ◽  
Author(s):  
Kerry E. Back
Keyword(s):  
Option Pricing ◽  
Interest Rates ◽  
Stochastic Volatility Model ◽  
Futures Contracts ◽  
Expectations Hypothesis ◽  
Forward Measure ◽  
Volatility Models ◽  
Volatility Model ◽  
Forward Prices ◽  
Exchange Options

Forward measures are defined. Forward and futures contracts are explained. The spot‐forward parity formula is derived. A forward price is a martingale under the forward measure. A futures price is a martingale under a risk neutral probability. Forward prices equal futures prices when interest rates are nonrandom. The expectations hypothesis is explained. The option pricing formulas of Margabe (exchange options), Black (options on forwards), and Merton (random interest rates) are derived. Implied volatilities and local volatility models are explained. Heston’s stochastic volatility model is derived.

FORWARD START OPTIONS UNDER STOCHASTIC VOLATILITY AND STOCHASTIC INTEREST RATES

2009 ◽  
Vol 12 (02) ◽  
pp. 209-225 ◽  
Author(s):  
REHEZ AHLIP ◽  
MAREK RUTKOWSKI
Keyword(s):  
Interest Rates ◽  
Stochastic Volatility ◽  
Stock Return ◽  
Probabilistic Approach ◽  
Stochastic Volatility Model ◽  
Stochastic Interest Rates ◽  
European Call Option ◽  
Volatility Model ◽  
Stochastic Interest ◽  
Instantaneous Volatility

Forward start options are examined in Heston's (Review of Financial Studies6 (1993) 327–343) stochastic volatility model with the CIR (Econometrica53 (1985) 385–408) stochastic interest rates. The instantaneous volatility and the instantaneous short rate are assumed to be correlated with the dynamics of stock return. The main result is an analytic formula for the price of a forward start European call option. It is derived using the probabilistic approach combined with the Fourier inversion technique, as developed in Carr and Madan (Journal of Computational Finance2 (1999) 61–73).

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