The pricing of foreign currency options under jump‐diffusion processes

We derive results similar to Bo et al. (2010), but in the case of dynamics of the FX rate driven by a general Merton jump-diffusion process. The main results of our paper are as follows: 1) formulas for the Esscher transform parameters which ensure that the martingale condition for the discounted foreign exchange rate is a martingale for a general Merton jump-diffusion process are derived; using the values of these parameters we proceed to a risk-neural measure and provide new formulas for the distribution of jumps, the mean jump size, and the Poisson Process intensity with respect to the measure; pricing formulas for European foreign exchange call options have been given as well; 2) obtained formulas are applied to the case of the exponential processes; 3) numerical simulations of European call foreign exchange option prices for different parameters are also provided.

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“…Putting (33) to (32) and taking into account characteristic function of Brownian motion (see (15)) we have:…”

Section: Currency Option Pricing For Merton Jump-diffusion Processesmentioning

confidence: 99%

Currency Derivatives Pricing for Markov-Modulated Merton Jump-Diffusion Spot Forex Rate

Swishchuk¹,

Tertychnyi²,

Hoang³

2014

JMF

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“…Pricing European Options on the exchange rate was developed by Garman and Kohlhagen [ 35 ]. In later works, the Garman–Kohlhagen model was extended in various directions [ 36 , 37 , 38 , 39 ].…”

Section: Introductionmentioning

confidence: 99%

Entropic Dynamics of Exchange Rates and Options

Abedi

Bartolomeo

2019

Entropy

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An Entropic Dynamics of exchange rates is laid down to model the dynamics of foreign exchange rates, FX, and European Options on FX. The main objective is to represent an alternative framework to model dynamics. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. Entropic Dynamics is an application of entropic inference, which is equipped with the entropic notion of time to model dynamics. The scale invariance is a symmetry of the dynamics of exchange rates, which is manifested in our formalism. To make the formalism manifestly invariant under this symmetry, we arrive at choosing the logarithm of the exchange rate as the proper variable to model. By taking into account the relevant information about the exchange rates, we derive the Geometric Brownian Motion, GBM, of the exchange rate, which is manifestly invariant under the scale transformation. Securities should be valued such that there is no arbitrage opportunity. To this end, we derive a risk-neutral measure to value European Options on FX. The resulting model is the celebrated Garman-Kohlhagen

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“…Watt [1], Daal [2], and Pitarbarg [3] developed call option currency valuation models, which did not account for the variation of foreign currencies with time. Schogl [4] included time distribution in a market-based model, while Mikkelson [5], Ahn [6] and Garman, etc. [7] introduced jumps into call valuation to account for discontinuities in the movement of foreign currencies with time.…”

Section: Introductionmentioning

confidence: 99%

The Valuation of Currency Put Options

Abraham¹

2018

TEL

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Investors who seek to profit from depreciating currencies may invest in put options. Upon option exercise, the currency is sold at a high price, and then purchased at the lower future currency value, resulting in a gain for the put buyer. A series of such transactions yields a stream of income for the put investor. Alternatively, the investor could short sell the currency, reaping gains from the difference between the high short sale price and the low future purchase price. This paper derives the theoretical formulations for combined short sale and puts purchase strategies for the US dollar, the Euro, the Australian dollar and the New Zealand dollar, and the Mexican peso. Utility functions are based upon an assumption of declining risk aversio with negative rescale factors and positive threshold factors in a hyperbolic cosine distribution. This distribution intersects with the cosine distribution of short sale prices on the U. S. dollar, the lognormal distribution of short sale prices on the Euro, the Weiner process for shorts on the Australian dollar and the New Zealand dollar, and the Laplace currency distribution for peso shorts. Similar utility functions intersect with Levy-Khintchine jump processes to provide put option prices for each type of foreign currency.

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The pricing of foreign currency options under jump‐diffusion processes

Cited by 16 publications

References 34 publications

Currency Derivatives Pricing for Markov-Modulated Merton Jump-Diffusion Spot Forex Rate

Currency Derivatives Pricing for Markov-Modulated Merton Jump-Diffusion Spot Forex Rate

Entropic Dynamics of Exchange Rates and Options

The Valuation of Currency Put Options

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