Derivatives pricing is quantitative finance’s oldest deep-math tradition, and this hub holds the collection’s densest concentration of stochastic calculus. The research spans pricing models (jump diffusions, stochastic volatility, rough volatility), numerical methods (Monte Carlo variants, PDE solvers, ML surrogates for high-dimensional pricing), and the newer deep hedging literature that learns hedge ratios directly under transaction costs.
The quadrant system earns its keep here: much of this work is mathematically airtight but empirically untested (“Lab Rats” in our scoring), which is fine for pricing engines and dangerous for trading claims. When a paper proposes a new model, the questions that matter are calibration stability — does it fit today’s surface without absurd parameters tomorrow — and hedging performance out of sample, not merely in-sample fit to option quotes.
Related hubs: Volatility Modeling, Fixed Income & Rates, Machine Learning for Forecasting.
In this analysis we determine factors driving the cross-sectional variation in uninsured deposits during the interest rate raising cycle of 2022 to 2023. The goal of our analysis is to determine whether banks proactively managed deposit run risk prior to the hiking cycle which produced the 2023 Regi
We revisit the classical topic of quadratic and linear mean-variance equilibria with both financial and real assets. The novelty of our results is that they are the first allowing for equilibrium prices driven by general semimartingales and hold in discrete as well as continuous time. For agents wit
This paper solves a recursive optimal stopping problem with Poisson stopping constraints using the penalized backward stochastic differential equation (PBSDE) with jumps. Stopping in this problem is only allowed at Poisson random intervention times, and jumps play a significant role not only through
In the short time to maturity limit it is proved that for the conditionally lognormal SABR model the zero vanna implied volatility is a lower bound for the volatility swap strike. The result is valid for all values of the correlation parameter and is a sharper lower bound than the at-the-money impli
This paper studies the pricing and hedging of derivatives in frictionless and competitive, but incomplete jump-diffusion markets. A unique equivalent martingale measure (EMM) is obtained using filtration reduction to a fictitious complete market. This unique EMM in the fictitious market is uplifted
We study a continuous-time Markowitz mean-variance portfolio selection model in which a naive agent, unaware of the underlying time-inconsistency, continuously reoptimizes over time. We define the resulting naive policies through the limit of discretely naive policies that are committed only in very
This paper researches the problem of purchasing deferred term insurance in the context of financial planning to maximize the probability of achieving a personal financial goal. Specifically, our study starts from the perspective of hedging death risk and longevity risk, and considers the purchase of
We study scaled trinomial models converging to the Black–Scholes model, and analyze exponential certainty-equivalent prices for path-dependent European options. As the number of trading dates $n$ tends to infinity and the risk aversion is scaled as $nl$ for a fixed constant $l>0$, we derive a nontr
Options are contingent claims regarding the value of underlying assets. The Black-Scholes formula provides a road map for pricing these options in a risk-neutral setting, justified by a delta hedging argument in which countervailing positions of appropriate size are taken in the underlying asset. Ho
We consider the problem of optimal investment with random endowment in a Black–Scholes market for an agent with constant relative risk aversion. Using duality arguments, we derive an explicit expression for the optimal trading strategy, which can be decomposed into the optimal strategy in the absenc
We consider an economy composed of different risk profile regions wishing to be hedged against a disaster risk using multi-region catastrophe insurance. Such catastrophic events inherently have a systemic component; we consider situations where the insurer faces a non-zero probability of insolvency.
Financial derivative pricing is a significant challenge in finance, involving the valuation of instruments like options based on underlying assets. While some cases have simple solutions, many require complex classical computational methods like Monte Carlo simulations and numerical techniques. Howe
We consider the pricing and hedging of counterparty credit risk and funding when there is no possibility to hedge the jump to default of either the bank or the counterparty. This represents the situation which is most often encountered in practice, due to the absence of quoted corporate bonds or CDS
This paper examines a semi-analytical approach for pricing American options in time-inhomogeneous models characterized by negative interest rates (for equity/FX) or negative convenience yields (for commodities/cryptocurrencies). Under such conditions, exercise boundaries may exhibit a “floating” str
The gas fee, paid for inclusion in the blockchain, is analyzed in two parts. First, we consider how effort in terms of resources required to process and store a transaction turns into a gas limit, which, through a fee, comprised of the base and priority fee in the current version of Ethereum, is con
This paper analyzes a problem of optimal static hedging using derivatives in incomplete markets. The investor is assumed to have a risk exposure to two underlying assets. The hedging instruments are vanilla options written on a single underlying asset. The hedging problem is formulated as a utility
This paper is a supplement to our recent paper Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in Lévy models". We introduce the class of regime-switching Lévy models with memory, which take into account the evolution of the stochastic parameters in
In this paper, we consider the discrete-time setting, and the market model described by (S,F,T)$. Herein F is the ``public" flow of information which is available to all agents overtime, S is the discounted price process of d-tradable assets, and T is an arbitrary random time whose occurrence might
This note revisits the SWIFT method based on Shannon wavelets to price European options under models with a known characteristic function in 2023. In particular, it discusses some possible improvements and exposes some concrete drawbacks of the method.
Hedge fund managers with the first-loss scheme charge a management fee, a performance fee and guarantee to cover a certain amount of investors’ potential losses. We study how parties can choose a mutually preferred first-loss scheme in a hedge fund with the manager’s first-loss deposit and investors