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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 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…
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…
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…
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…
We study an OTC FX market-making problem, built on the Avellaneda-Stoikov tradition, in which a dealer streams size-dependent quotes on a discrete ladder and manages inventory risk over a finite horizon under Poisson arrivals of trade requests. Adverse selection is modelled through latency-driven price moves over a delay window, represented by Gaussian marks whose conditional means can depend on the quoted spread, ca…
Missing data is a common problem in finance and often requires methods to fill in the gaps, or in other words, imputation. In this work, we focused on the imputation of missing implied volatilities for FX options. Prior work has used variational autoencoders (VAEs), a neural network-based approach, to solve this problem; however, using stronger classical baselines such as Heston with jumps can significantly outperfor…
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…
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 …
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.
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, …
This paper investigates the hedging performance of pegged foreign exchange market in a regime switching (RS) model introduced in a recent paper by Drapeau, Wang and Wang (2019). We compare two prices, an exact solution and first order approximation and provide the bounds for the error. We provide exact RS delta, approximated RS delta as well as mean variance hedging strategies for this specific model and compare thei…
We have discovered 12 independent new empirical scaling laws in foreign exchange data-series that hold for close to three orders of magnitude and across 13 currency exchange rates. Our statistical analysis crucially depends on an event-based approach that measures the relationship between different types of events. The scaling laws give an accurate estimation of the length of the price-curve coastline, which turns ou…
A CTA is a manager — often CFTC/NFA registered — that runs client money in futures and options on futures, long and short, across rates, FX, equities, and commodities.
The standard G10/EM carry trade run as a vol-targeted futures/forward sleeve beside FX trend — coupon versus crash.
A program that risks money across the four big futures groups — equity indices, bonds/STIR, FX, and commodities — rather than a single pit.
Currency futures and NDF/forwards — G10 trend, EM, and sometimes a carry overlay — the most liquid two-way sleeve in the complex.
Risk Reversal — Call-put spread package measuring directional skew in FX and equity options.
Current Account Balance — External imbalance measure linking domestic savings-investment gaps to currency pressure.
Nonfarm Payrolls — The headline US jobs report that routinely moves rates, FX, and equity index volatility.
Original Sin EM Debt — Inability to borrow long-term in local currency, raising external vulnerability.
Bankhaus Herstatt failed in 1974 between the two legs of FX settlement, creating Herstatt risk — the reason we have CLS and why FX is a payments-system problem.
The Plaza Accord was a coordinated 1985 G5 intervention to weaken the dollar after a brutal early-1980s USD squeeze — not a crash, but a regime change in FX that re-priced US manufacturing and later fed Japan’s bubble politics.
On 15 January 2015 the SNB abandoned the 1.20 EUR/CHF floor in minutes — a peg break that wiped FX brokers and carry books that had treated the floor as a free option.
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.
Carry Trade FX — Funding low-yield currencies to invest in high-yielders — pro-cyclical and crash-prone.
A peg is a policy that holds the exchange rate to a target or band — a promise that spends reserves and rates when the market disagrees.
Currency Reserves Adequacy — Whether EM authorities can defend pegs or smooth disorderly depreciations.
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.
FX Implied Volatility — Option-implied uncertainty for currency pairs, key for hedging and risk budgeting.
Interest-rate parity links interest differentials to forward FX — covered IRP is an arb; uncovered is a hypothesis the carry trade fades.
A pip is the conventional smallest FX increment — usually 0.0001 for most pairs and 0.01 for JPY pairs.
Purchasing Power Parity — Long-horizon FX anchor based on relative price levels, often slow to converge.
Real Effective Exchange Rate — Trade-weighted currency adjusted for inflation differentials.
Terms of Trade Shock — Relative export-import price shifts altering growth and currency paths.
Twin Deficits — Combined fiscal and current-account deficits pressuring currency and term premium.
Uncovered Interest Parity — Hypothesis that high-yield currencies depreciate as carry accrues.
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.
Long currencies that appreciated over the lookback, short those that depreciated — cross-sectional FX momentum.
Long undervalued currencies and short overvalued ones versus purchasing-power parity or real-rate gaps — FX value, slow and mean-reverting.
Long high-yield currencies, short low-yield currencies — harvest the forward premium that uncovered interest parity says should not persist.
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.
Carry Trade FX — Funding low-yield currencies to invest in high-yielders — pro-cyclical and crash-prone.
A CTA is a manager — often CFTC/NFA registered — that runs client money in futures and options on futures, long and short, across rates, FX, equities, and commodities.
Funding stress signal derived from FX swap pricing distortions and balance sheet constraints.
The standard G10/EM carry trade run as a vol-targeted futures/forward sleeve beside FX trend — coupon versus crash.
Long currencies that appreciated over the lookback, short those that depreciated — cross-sectional FX momentum.
A peg is a policy that holds the exchange rate to a target or band — a promise that spends reserves and rates when the market disagrees.
Currency Reserves Adequacy — Whether EM authorities can defend pegs or smooth disorderly depreciations.
Long undervalued currencies and short overvalued ones versus purchasing-power parity or real-rate gaps — FX value, slow and mean-reverting.
A program that risks money across the four big futures groups — equity indices, bonds/STIR, FX, and commodities — rather than a single pit.
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.
Long high-yield currencies, short low-yield currencies — harvest the forward premium that uncovered interest parity says should not persist.
Currency futures and NDF/forwards — G10 trend, EM, and sometimes a carry overlay — the most liquid two-way sleeve in the complex.
FX Implied Volatility — Option-implied uncertainty for currency pairs, key for hedging and risk budgeting.
Bankhaus Herstatt failed in 1974 between the two legs of FX settlement, creating Herstatt risk — the reason we have CLS and why FX is a payments-system problem.
Interest-rate parity links interest differentials to forward FX — covered IRP is an arb; uncovered is a hypothesis the carry trade fades.
Nonfarm Payrolls — The headline US jobs report that routinely moves rates, FX, and equity index volatility.
A pip is the conventional smallest FX increment — usually 0.0001 for most pairs and 0.01 for JPY pairs.
The Plaza Accord was a coordinated 1985 G5 intervention to weaken the dollar after a brutal early-1980s USD squeeze — not a crash, but a regime change in FX that re-priced US manufacturing and later fed Japan’s bubble politics.
Purchasing Power Parity — Long-horizon FX anchor based on relative price levels, often slow to converge.
Real Effective Exchange Rate — Trade-weighted currency adjusted for inflation differentials.
Risk Reversal — Call-put spread package measuring directional skew in FX and equity options.