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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 …
This paper acts as a collection of various trading strategies and useful pieces of market information that might help to implement such strategies. This list is meant to be comprehensive (though by no means exhaustive) and hence we only provide pointers and give further sources to explore each strategy further. To set the stage for this exploration, we consider the factors that determine good and bad trades, the noti…
Regarding the intraday sequence of high frequency returns of the S&P index as daily realizations of a given stochastic process, we first demonstrate that the scaling properties of the aggregated return distribution can be employed to define a martingale stochastic model which consistently replicates conditioned expectations of the S&P 500 high frequency data in the morning of each trading day. Then, a more general fo…
Constant product markets with concentrated liquidity (CL) are the most popular type of automated market makers. In this paper, we characterise the continuous-time wealth dynamics of strategic LPs who dynamically adjust their range of liquidity provision in CL pools. Their wealth results from fee income, the value of their holdings in the pool, and rebalancing costs. Next, we derive a self-financing and closed-form op…
The standard approach for compensating liquidity providers on many decentralized exchanges (DEX) for serving as counter-party to swaps is through charging a small percentage of fees. The expected payoff from the cash flow of this mode of market making has yet to be mathematically formulated in terms of volatility in the existing literature. We provide here a preliminary derivation of the payoff formula, by making the…
This paper considers liquidity as an explanation for the positive association between expected idiosyncratic volatility (IV) and expected stock returns. Liquidity costs may affect the stock returns, through bid-ask bounce and other microstructure-induced noise, which will affect the estimation of IV. We use a novel method (developed by Weaver, 1991) to eliminate microstructure influences from stock closing price-base…
We review different approaches for measuring the impact of liquidity on CDS prices. We start with reduced form models incorporating liquidity as an additional discount rate. We review Chen, Fabozzi and Sverdlove (2008) and Buhler and Trapp (2006, 2008), adopting different assumptions on how liquidity rates enter the CDS premium rate formula, about the dynamics of liquidity rate processes and about the credit-liquidit…
We study a one period limit order market with informed traders, noise traders, and competitive liquidity suppliers, in which the number of informed traders is random. Liquidity suppliers know the distribution of the informed trader count, but not its realization, and therefore face uncertainty about both the presence and the intensity of informed trading. We characterize equilibrium by a fixed point integral equation…
In this paper, we investigate a portfolio investment problem under volatility uncertainty and short-sale constraints market via sublinear expectation which is used to model volatility uncertainty. We assume the stocks admit volatility uncertainty. Thus the related portfolio has upper variance (maximum risk) and lower variance (minimum risk). By introducing a risk factor $w$ to conduct coupled modeling of the maximum …
We propose a profitable trading strategy for the cryptocurrency market based on grid trading. Starting with an analysis of the expected value of the traditional grid strategy, we show that under simple assumptions, its expected return is essentially zero. We then introduce a novel Dynamic Grid-based Trading (DGT) strategy that adapts to market conditions by dynamically resetting grid positions. Our backtesting result…
We investigate portfolio optimization in financial markets from a trading and risk management perspective. We term this task Risk-Aware Trading Portfolio Optimization (RATPO), formulate the corresponding optimization problem, and propose an efficient Risk-Aware Trading Swarm (RATS) algorithm to solve it. The key elements of RATPO are a generic initial portfolio P, a specific set of Unique Eligible Instruments (UEIs),…
There is substantial empirical evidence showing the fundamental portfolio outperforming the market portfolio. Here a theoretical foundation is laid that supports this empirical research. Assuming stock prices revert around fundamental prices with sufficient strength and symmetry, the fundamental portfolio outperforms the market portfolio in expectation. If reversion toward the fundamental price is not sufficiently st…
Designing an optimum portfolio that allocates weights to its constituent stocks in a way that achieves the best trade-off between the return and the risk is a challenging research problem. The classical mean-variance theory of portfolio proposed by Markowitz is found to perform sub-optimally on the real-world stock market data since the error in estimation for the expected returns adversely affects the performance of…
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 …
In this paper, we employ the Heston stochastic volatility model to describe the stock's volatility and apply the model to derive and analyze the optimal trading strategies for dealers in a security market. We also extend our study to option market making for options written on stocks in the presence of stochastic volatility. Mathematically, the problem is formulated as a stochastic optimal control problem and the con…
We study the problem of the optimal execution of a large trade in the presence of nonlinear transient impact. We propose an approach based on homotopy analysis, whereby a well behaved initial strategy is continuously deformed to lower the expected execution cost. We find that the optimal solution is front loaded for concave impact and that its expected cost is significantly lower than that of conventional strategies.…
Kyle (1985) builds a pioneering and influential model, in which an insider with long-lived private information submits an optimal order in each period given the market maker's pricing rule. An inconsistency exists to some extent in the sense that the ``constant pricing rule " actually assumes an adaptive expected price with pricing rule given before insider making the decision, and the ``market efficiency" condition,…
Analytical, free of time consuming Monte Carlo simulations, framework for credit portfolio systematic risk metrics calculations is presented. Techniques are described that allow calculation of portfolio-level systematic risk measures (standard deviation, VaR and Expected Shortfall) as well as allocation of risk down to individual transactions. The underlying model is the industry standard multi-factor Merton-type mod…
Copper price is widely used as a proxy for industrial activity, manufacturing demand, and global growth expectations.
US 10-Year Breakeven Inflation reflects the inflation rate implied by the gap between nominal Treasuries and TIPS, serving as a market-based gauge of long-term inflation expectations.
The 2s10s Treasury curve measures the spread between 10-year and 2-year Treasury yields and is a key indicator of growth expectations, policy path, and term structure dynamics.
FRA-OIS spread measures the difference between interbank funding expectations and overnight indexed swap rates, often used as a gauge of banking and short-term funding stress.
The term structure of interest rates across maturities, used to read growth, liquidity, and stress expectations.
Forward Guidance — How central bank language shapes term premium and front-end rate expectations before actual policy moves.
Consumer Confidence Index — Household expectations that influence spending, labor supply, and political pressure on policy.
Inflation Expectations Survey — Household and market-based expectations that can de-anchor if policy credibility erodes.
Primary Dealer Survey — Desk-level policy expectations that front-run official communications.
Expectations Hypothesis — Theory that long rates equal expected short rates path.
The 2s10s Treasury curve measures the spread between 10-year and 2-year Treasury yields and is a key indicator of growth expectations, policy path, and term structure dynamics.
Consumer Confidence Index — Household expectations that influence spending, labor supply, and political pressure on policy.
Copper price is widely used as a proxy for industrial activity, manufacturing demand, and global growth expectations.
Expectations Hypothesis — Theory that long rates equal expected short rates path.
Forward Guidance — How central bank language shapes term premium and front-end rate expectations before actual policy moves.
FRA-OIS spread measures the difference between interbank funding expectations and overnight indexed swap rates, often used as a gauge of banking and short-term funding stress.
Inflation Expectations Survey — Household and market-based expectations that can de-anchor if policy credibility erodes.
Primary Dealer Survey — Desk-level policy expectations that front-run official communications.
US 10-Year Breakeven Inflation reflects the inflation rate implied by the gap between nominal Treasuries and TIPS, serving as a market-based gauge of long-term inflation expectations.
The term structure of interest rates across maturities, used to read growth, liquidity, and stress expectations.