# Pricing FX Options under Intermediate Currency

@article{Maurer2019PricingFO, title={Pricing FX Options under Intermediate Currency}, author={Samuel Maurer and Timothy Sharp and Michael V. Tretyakov}, journal={arXiv: Mathematical Finance}, year={2019} }

We introduce a new pricing mechanism for FX options, which is based on the idea of an intermediate pseudo-currency market. This approach allows us to price options on all FX markets simultaneously under the same risk-neutral measure which ensures consistency of FX option prices across all markets. In particular, it is sufficient to calibrate a model to the volatility smile on the domestic market as, due to the consistency of pricing formulas, the model automatically reproduces the correct smile… Expand

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SHOWING 1-10 OF 28 REFERENCES

A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options

- Economics
- 1993

I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and… Expand

The Stochastic Intrinsic Currency Volatility Model: A Consistent Framework for Multiple FX Rates and Their Volatilities

- Economics
- 2012

Abstract The SABR and the Heston stochastic volatility models are widely used for foreign exchange (FX) option pricing. Although they are able to reproduce the market's volatility smiles and skews… Expand

FX Options and Smile Risk

- Economics
- 2010

The FX options market represents one of the most liquid and strongly competitive markets in the world, and features many technical subtleties that can seriously harm the uninformed and unaware… Expand

The Value of an Option to Exchange One Asset for Another

- Economics
- 1978

SOME COMMON FINANCIAL ARRANGEMENTS are equivalent to options to exchange one risky asset for another: the investment adviser's performance incentive fee, the general margin account, the exchange… Expand

MANAGING SMILE RISK

- 2002

Market smiles and skews are usually managed by using local volatility models a la Dupire. We discover that the dynamics of the market smile predicted by local vol models is opposite of observed… Expand

FX volatility smile construction

- Economics
- 2012

The foreign exchange options market is one of the largest and most liquid OTC derivative markets in the world. Surprisingly, very little is known in the academic literature about the construction of… Expand

An Affine Multicurrency Model with Stochastic Volatility and Stochastic Interest Rates

- Economics, Computer Science
- SIAM J. Financial Math.
- 2014

We introduce a tractable multicurrency model with stochastic volatility and correlated stochastic interest rates that takes into account the smile in the foreign exchange (FX) market and the… Expand

The Moment Formula for Implied Volatility at Extreme Strikes

- Mathematics
- 2004

Consider options on a nonnegative underlying random variable with arbitrary distribution. In the absence of arbitrage, we show that at any maturity T, the large-strike tail of the Black-Scholes… Expand

Moment generating functions and normalized implied volatilities: unification and extension via Fukasawa’s pricing formula

- Mathematics, Economics
- 2017

We extend the model-free formula of Fukasawa [Math. Finance, 2012, 22, 753–762] for , where is the log-price of an asset, to functions of exponential growth. The resulting integral representation is… Expand

On the Heston Model with Stochastic Interest Rates

- Computer Science, Economics
- SIAM J. Financial Math.
- 2011

Two different approximations of the Heston hybrid model with stochastic interest rates driven by Hull-White or Cox-Ingersoll-Ross processes are presented in order to obtain the characteristic functions. Expand