Pricing currency options in the Heston/CIR double exponential jump-diffusion model

2017 ◽  
Vol 04 (01) ◽  
pp. 1750013 ◽  
Author(s):  
Rehez Ahlip ◽  
Laurence A. F. Park ◽  
Ante Prodan
Keyword(s):  
Exchange Rate ◽  
Interest Rates ◽  
Analytical Formula ◽  
Jump Diffusion ◽  
Stochastic Volatility Model ◽  
Currency Options ◽  
Volatility Model ◽  
Double Exponential ◽  
Jump Diffusion Model ◽  
The Exchange Rate

We examine currency options in the double exponential jump-diffusion version of the Heston stochastic volatility model for the exchange rate. We assume, in addition, that the domestic and foreign stochastic interest rates are governed by the CIR dynamics. The instantaneous volatility is correlated with the dynamics of the exchange rate return, whereas the domestic and foreign short-term rates are assumed to be independent of the dynamics of the exchange rate and its volatility. The main result furnishes a semi-analytical formula for the price of the European currency call option in the hybrid foreign exchange/interest rates model.

scholarly journals Pricing FX Options in the Heston/CIR Jump-Diffusion Model with Log-Normal and Log-Uniform Jump Amplitudes

2015 ◽  
Vol 2015 ◽  
pp. 1-15
Author(s):  
Rehez Ahlip ◽  
Ante Prodan
Keyword(s):  
Exchange Rate ◽  
Interest Rates ◽  
Foreign Exchange ◽  
Jump Diffusion ◽  
Stochastic Volatility Model ◽  
Volatility Model ◽  
Jump Diffusion Model ◽  
The Exchange Rate ◽  
Log Normal ◽  
Instantaneous Volatility

We examine foreign exchange options in the jump-diffusion version of the Heston stochastic volatility model for the exchange rate with log-normal jump amplitudes and the volatility model with log-uniformly distributed jump amplitudes. We assume that the domestic and foreign stochastic interest rates are governed by the CIR dynamics. The instantaneous volatility is correlated with the dynamics of the exchange rate return, whereas the domestic and foreign short-term rates are assumed to be independent of the dynamics of the exchange rate and its volatility. The main result furnishes a semianalytical formula for the price of the foreign exchange European call option.

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.

scholarly journals A Hull and White Formula for a General Stochastic Volatility Jump-Diffusion Model with Applications to the Study of the Short-Time Behavior of the Implied Volatility

2008 ◽  
Vol 2008 ◽  
pp. 1-17 ◽  
Author(s):  
Elisa Alòs ◽  
Jorge A. León ◽  
Monique Pontier ◽  
Josep Vives
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Asset Price ◽  
Jump Diffusion ◽  
Stochastic Volatility Model ◽  
Time Behavior ◽  
Volatility Model ◽  
Jump Diffusion Model ◽  
White Type ◽  
Short Time

We obtain a Hull and White type formula for a general jump-diffusion stochastic volatility model, where the involved stochastic volatility process is correlated not only with the Brownian motion driving the asset price but also with the asset price jumps. Towards this end, we establish an anticipative Itô's formula, using Malliavin calculus techniques for Lévy processes on the canonical space. As an application, we show that the dependence of the volatility process on the asset price jumps has no effect on the short-time behavior of the at-the-money implied volatility skew.

FOURIER TRANSFORM METHOD WITH AN ASYMPTOTIC EXPANSION APPROACH: AN APPLICATION TO CURRENCY OPTIONS

2008 ◽  
Vol 11 (04) ◽  
pp. 381-401 ◽  
Author(s):  
AKIHIKO TAKAHASHI ◽  
KOHTA TAKEHARA
Keyword(s):  
Fourier Transform ◽  
Asymptotic Expansion ◽  
Interest Rates ◽  
Jump Diffusion ◽  
Characteristic Functions ◽  
Currency Options ◽  
Transform Method ◽  
Fourier Transform Method ◽  
Libor Market Model ◽  
Jump Diffusion Model

This paper develops a Fourier transform method with an asymptotic expansion approach for option pricing. The method is applied to European currency options with a libor market model of interest rates and jump-diffusion stochastic volatility models of spot exchange rates. In particular, we derive closed-form approximation formulas of the characteristic functions of log-prices of the underlying assets and the prices of currency options based on a third order asymptotic expansion scheme; we use a jump-diffusion model with a mean-reverting stochastic variance process such as in Heston [7]/Bates [1] and log-normal market models for domestic and foreign interest rates. Finally, the validity of our method is confirmed through numerical examples.

scholarly journals Option Pricing under Double Stochastic Volatility Model with Stochastic Interest Rates and Double Exponential Jumps with Stochastic Intensity

2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
Ying Chang ◽  
Yiming Wang
Keyword(s):  
Option Pricing ◽  
Interest Rates ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Stochastic Interest Rates ◽  
Stochastic Intensity ◽  
Volatility Model ◽  
Double Exponential ◽  
Stochastic Interest ◽  
The Impact

We present option pricing under the double stochastic volatility model with stochastic interest rates and double exponential jumps with stochastic intensity in this article. We make two contributions based on the existing literature. First, we add double stochastic volatility to the option pricing model combining stochastic interest rates and jumps with stochastic intensity, and we are the first to fill this gap. Second, the stochastic interest rate process is presented in the Hull–White model. Some authors have concentrated on hybrid models based on various asset classes in recent years. Therefore, we build a multifactor model with the term structure of stochastic interest rates. We also approximated the pricing formula for European call options by applying the COS method and fast Fourier transform (FFT). Numerical results display that FFT and the COS method are much faster than the numerical integration approach used for obtaining the semi-closed form prices. The COS method shows higher accuracy, efficiency, and stability than FFT. Therefore, we use the COS method to investigate the impact of the parameters in the stochastic jump intensity process and the existence of the process on the call option prices. We also use it to examine the impact of the parameters in the interest rate process on the call option prices.

scholarly journals A Theory of Foreign Exchange Interventions

2021 ◽  
Author(s):  
Sebastián Fanelli ◽  
Ludwig Straub
Keyword(s):  
Exchange Rate ◽  
Central Bank ◽  
Interest Rates ◽  
Open Economy ◽  
Small Open Economy ◽  
Bond Markets ◽  
Pecuniary Externality ◽  
Optimal Intervention ◽  
The Exchange Rate ◽  
Intervention Policy

Abstract We study a real small open economy with two key ingredients (1) partial segmentation of home and foreign bond markets and (2) a pecuniary externality that makes the real exchange rate excessively volatile in response to capital flows. Partial segmentation implies that, by intervening in the bond markets, the central bank can affect the exchange rate and the spread between home- and foreign-bond yields. Such interventions allow the central bank to address the pecuniary externality, but they are also costly, as foreigners make carry trade profits. We analytically characterize the optimal intervention policy that solves this trade-off: (1) the optimal policy leans against the wind, stabilizing the exchange rate; (2) it involves smooth spreads but allows exchange rates to jump; (3) it partly relies on “forward guidance,” with non-zero interventions even after the shock has subsided; (4) it requires credibility, in that central banks do not intervene without commitment. Finally, we shed light on the global consequences of widespread interventions, using a multi-country extension of our model. We find that, left to themselves, countries over-accumulate reserves, reducing welfare and leading to inefficiently low world interest rates.

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.

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