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As the FX markets continue to evolve, many institutions have started offering passive access to their internal liquidity pools. Market makers act as principal and have the opportunity to fill those orders as part of their risk management, or they may choose to adjust pricing to their external OTC franchise to facilitate the matching flow. It is, a priori, unclear how the strategies managing internal liquidity should …
We develop an optimal currency hedging strategy for fund managers who own foreign assets to choose the hedge tenors that maximize their FX carry returns within a liquidity risk constraint. The strategy assumes that the offshore assets are fully hedged with FX forwards. The chosen liquidity risk metric is Cash Flow at Risk (CFaR). The strategy involves time-dispersing the total nominal hedge value into future time buc…
Credit Default Swaps (CDS) on a reference entity may be traded in multiple currencies, in that protection upon default may be offered either in the domestic currency where the entity resides, or in a more liquid and global foreign currency. In this situation currency fluctuations clearly introduce a source of risk on CDS spreads. For emerging markets, but in some cases even in well developed markets, the risk of dram…
We develop a method to decompose the PnL of a portfolio of assets into four parts: (a) PnL due to FX rate changes, (b) PnL due to interest rate changes, (c) carry gain due to time passing, (d) PnL due to residual market risk changes (credit risk, liquidity risk, volatility risk etc.). We demonstrate the usefulness of our approach by decomposing the performance of an FX- and interest rate-hedged negative basis positio…
In FX cash markets, market makers provide liquidity to clients for a wide variety of currency pairs. Because of flow uncertainty and market volatility, they face inventory risk. To mitigate this risk, they typically skew their prices to attract or divert the flow and trade with their peers on the dealer-to-dealer segment of the market for hedging purposes. This paper offers a mathematical framework to FX dealers will…
Dealers make money by providing liquidity to clients but face flow uncertainty and thus price risk. They can efficiently skew their prices and wait for clients to mitigate risk (internalization), or trade with other dealers in the open market to hedge their position and reduce their inventory (externalization). Of course, the better control associated with externalization comes with transaction costs and market impac…
We develop an expansion approach for the pricing of European quanto options written on LIBOR rates (of a foreign currency). We derive the dynamics of the system of foreign LIBOR rates under the domestic forward measure and then consider the price of the quanto option. In order to take the skew/smile effect observed in fixed income and FX markets into account, we consider local volatility models for both the LIBOR and…
When trading American and Asian options in the FX derivatives market, banks must calculate prices using a complex mathematical model. It is often observed that different models produce varying prices for the same exotic option, which violates the non-arbitrage requirement of derivative risk management. To address this issue, we have studied a fully parameterized local volatility model for pricing American/Asian optio…
This paper aims at solving FX market volatility modeling problem and finding the most becoming approach to this task. Validity of two competing approaches, classical econometric generalized conditional heteroscedasticity and mathematical (singular spectrum analysis and dynamical systems stability analysis) are tested on major currency pairs (EUR/USD, USD/JPY, GBP/USD) and unique high-frequency USD/RUB data. The study…
Finance is a particularly challenging application area for deep learning models due to low noise-to-signal ratio, non-stationarity, and partial observability. Non-deliverable-forwards (NDF), a derivatives contract used in foreign exchange (FX) trading, presents additional difficulty in the form of long-term planning required for an effective selection of start and end date of the contract. In this work, we focus on t…
In this note we discuss - in what is intended to be a pedagogical fashion - FX option pricing in target zones with attainable boundaries. The boundaries must be reflecting. The no-arbitrage requirement implies that the differential (foreign minus domestic) short-rate is not deterministic. When the band is narrow, we can pick the functional form of the FX rate process based on computational convenience. With a thought…
We study the local volatility function in the Foreign Exchange market where both domestic and foreign interest rates are stochastic. This model is suitable to price long-dated FX derivatives. We derive the local volatility function and obtain several results that can be used for the calibration of this local volatility on the FX option's market. Then, we study an extension to obtain a more general volatility model an…
A time series model for the FX dynamics is presented which takes into account structural peculiarities of the market, namely its heterogeneity and an information flow from long to short time horizons. The model emerges from an analogy between FX dynamics and hydrodynamic turbulence. The heterogeneity of the market is modeled in form of a multiplicative cascade of time scales ranging from several minutes to a few mont…
In recent years, the popularity of artificial intelligence has surged due to its widespread application in various fields. The financial sector has harnessed its advantages for multiple purposes, including the development of automated trading systems designed to interact autonomously with markets to pursue different aims. In this work, we focus on the possibility of recognizing and leveraging intraday price patterns …
We explore online inductive transfer learning, with a feature representation transfer from a radial basis function network formed of Gaussian mixture model hidden processing units to a direct, recurrent reinforcement learning agent. This agent is put to work in an experiment, trading the major spot market currency pairs, where we accurately account for transaction and funding costs. These sources of profit and loss, …
We adopt Deep Reinforcement Learning algorithms to design trading strategies for continuous futures contracts. Both discrete and continuous action spaces are considered and volatility scaling is incorporated to create reward functions which scale trade positions based on market volatility. We test our algorithms on the 50 most liquid futures contracts from 2011 to 2019, and investigate how performance varies across d…
Vanna-Volga is a popular method for the interpolation/extrapolation of volatility smiles. The technique is widely used in the FX markets context, due to its ability to consistently construct the entire Lognormal smile using only three Lognormal market quotes. However, the derivation of the Vanna-Volga method itself is free of distributional assumptions. With this is mind, it is surprising there have been no attempts …
This follow-up article analyzes the impact of foreign exchange option interpolation on the vanilla option implied volatilities. In particular different exact interpolations of broker quotes may lead to different implied volatilities at the 10$Δ$ and 25$Δ$ Puts and Calls.
Comparing DXY with an EM FX basket helps assess whether dollar strength is becoming a broader external-financing stress event for emerging markets.
DXY Index measures the U.S. dollar against a basket of major currencies and serves as a broad gauge of dollar strength and global financial conditions.
USD/JPY cross-currency basis measures the extra cost of obtaining dollars through FX swap markets and is a key indicator of offshore dollar funding stress.
Funding stress signal derived from FX swap pricing distortions and balance sheet constraints.
Foreign Exchange Intervention — Official buying or selling of currency to manage disorderly moves and imported inflation.
Nonfarm Payrolls — The headline US jobs report that routinely moves rates, FX, and equity index volatility.
Current Account Balance — External imbalance measure linking domestic savings-investment gaps to currency pressure.
Risk Reversal — Call-put spread package measuring directional skew in FX and equity options.
Carry Trade FX — Funding low-yield currencies to invest in high-yielders — pro-cyclical and crash-prone.
Real Effective Exchange Rate — Trade-weighted currency adjusted for inflation differentials.
Purchasing Power Parity — Long-horizon FX anchor based on relative price levels, often slow to converge.
FX Implied Volatility — Option-implied uncertainty for currency pairs, key for hedging and risk budgeting.
Currency Reserves Adequacy — Whether EM authorities can defend pegs or smooth disorderly depreciations.
Twin Deficits — Combined fiscal and current-account deficits pressuring currency and term premium.
Balance of Payments Crisis — Sudden stop in capital flows forcing adjustment through FX, rates, or austerity.
Capital Controls — Official restrictions on cross-border flows that reprice FX basis and investability.
FX Swap Implied Rate (FX).
Non-Deliverable Forward Market — Offshore price discovery for restricted currencies.
FX Forward Points (FX).
Trade Weighted Dollar — Broad USD strength index affecting global financial conditions.
Terms of Trade Shock — Relative export-import price shifts altering growth and currency paths.
Original Sin EM Debt — Inability to borrow long-term in local currency, raising external vulnerability.
Spot FX Rate (FX).
Covered Interest Parity — No-arbitrage link of forwards to interest rate differentials.
Uncovered Interest Parity — Hypothesis that high-yield currencies depreciate as carry accrues.
NEER Index (FX).
Bloomberg Dollar Spot Index (FX).
EM FX Basket (FX).
FX Volatility Surface (FX).
Risk Reversal FX (FX).
Butterfly FX Vol (FX).
NDF Market (FX).
Deliverable Forward FX (FX).
FX Swap (FX).
Currency Overlay (FX).
Intervention Risk FX (FX).
Adverse Selection FX spot — Execution quality, book dynamics, or venue microstructure concept.
Arrival Price Slippage FX spot — Execution quality, book dynamics, or venue microstructure concept.
Auction Imbalance FX spot (Microstructure).
Balance of Payments Crisis — Sudden stop in capital flows forcing adjustment through FX, rates, or austerity.
Barrier Cluster AUDUSD (FX).
Barrier Cluster EURUSD (FX).
Barrier Cluster GBPUSD (FX).
Barrier Cluster NZDUSD (FX).
Barrier Cluster USDBRL (FX).
Barrier Cluster USDCAD (FX).
Barrier Cluster USDCHF (FX).
Barrier Cluster USDCNH (FX).
Barrier Cluster USDINR (FX).
Barrier Cluster USDJPY (FX).
Barrier Cluster USDKRW (FX).
Barrier Cluster USDMXN (FX).
Barrier Cluster USDTRY (FX).
Barrier Cluster USDZAR (FX).
Black Market FX Premium (FX).
Bloomberg Dollar Spot Index (FX).
Butterfly FX Vol (FX).
Capital Control Premium — Extra premium in FX/asset prices under capital controls.
Capital Controls — Official restrictions on cross-border flows that reprice FX basis and investability.
Carry Signal AUDUSD (FX).