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.

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.

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 NOTE ON FOREIGN EXCHANGE INTERVENTIONS AT ZERO INTEREST RATES

2012 ◽  
Vol 16 (5) ◽  
pp. 802-817 ◽  
Author(s):  
Shigeru Iwata ◽  
Shu Wu
Keyword(s):  
Exchange Rate ◽  
Interest Rates ◽  
Foreign Exchange ◽  
Inflation Targeting ◽  
Policy Instrument ◽  
Liquidity Trap ◽  
Working Paper ◽  
Policy Goals ◽  
Rate Environment ◽  
The Exchange Rate

This note uses a nonlinear structural vector autoregression model to empirically investigate the effectiveness of official foreign exchange (FX) interventions in an economy when interest rates are constrained to the zero level, based on Japanese data in the 1990s. The model allows us to estimate the effects of FX interventions operating through different channels. We find that FX interventions are still capable of influencing the foreign exchange rate in a zero-interest-rate environment, even though their effects are greatly reduced by the zero lower bound on interest rates. Our results suggest that although it might be feasible to use the exchange rate as an alternative monetary policy instrument at zero interest rates as proposed by McCallum (Inflation Targeting and the Liquidity Trap, NBER working paper 8225, 2000), the exchange rate–based Taylor rule may not be very effective in achieving the ultimate policy goals.

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).

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.

scholarly journals The Dynamics of The Rupiah Exchange Rate in 2017-2020

2020 ◽  
Vol 5 (2) ◽  
pp. 1
Author(s):  
Muhammad Arief Aldila Susanto ◽  
Rr. Retno Retno Sugiharti
Keyword(s):  
Exchange Rate ◽  
Interest Rates ◽  
Money Supply ◽  
Foreign Exchange ◽  
Time Series Data ◽  
Series Data ◽  
Foreign Exchange Reserves ◽  
Long Run ◽  
Short Run ◽  
The Exchange Rate

<p align="justify">The exchange rate is one of the most important indicators in the economy. Moreover, with the increasing intensity of trade between countries, commonly referred to as international trade, this economic indicator becomes important for every country, including Indonesia. The change in the Indonesian exchange rate system to a free-floating system has made the exchange rate fluctuations more dynamic. The fluctuations are influenced by various factors, both internal and external. This study aims to determine the effect of the money supply (M<sub>2</sub>), foreign exchange reserves, SBI interest rates and world crude oil prices on the rupiah/dollar exchange rate in 2017-2020 both in the short run and in the long run. The data used is monthly time series data from 2017-2020. The analytical method used in this study is the Error Correction Model (ECM). The results in this study indicate that in the short run and long run the money supply and foreign exchange reserves variables have a significant effect on the rupiah exchange rate in 2017-2020.</p>

scholarly journals The Exchange Rate Volatility in Indonesia and Policy Response

2014 ◽  
Author(s):  
Ferry Syarifuddin
Keyword(s):  
Exchange Rate ◽  
Central Bank ◽  
Exchange Rates ◽  
Interest Rates ◽  
Foreign Exchange ◽  
Exchange Rate Volatility ◽  
Commodity Prices ◽  
Policy Response ◽  
Long Run ◽  
The Exchange Rate

High fluctuation of exchange rate in short horizon is obviously making economic activity more risky as uncertainty rises. Moreover, volatile exchange rates also make commodity prices, interest rates and a host of other variables more volatile as well. Although changes in long-run exchange rates tend to undergo relatively gradual shifts, in the shorter horizon, the exchange rate might be very volatile. Then there should be a systematic and measured policy to mitigate the foreign exchange fluctuations and to minimize the fluctuations as well as to drive it to its fundamental value. In this part, USD/IDR volatility is investigated using GARCH approach. The results reveal that, USD/IDR volatility in Indonesia is persistent. On the other hand, the following studies also present the outcomes of effectiveness of policy response by the Central Bank. Foreign-exchange sale interventions by the Central Bank lead conditional volatility of the USD/IDR to decrease slightly.

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.

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