Papers, ranked by score

Ordered by a blend of empirical rigor (60%) and math complexity (40%).

Explicit Caplet Implied Volatilities for Quadratic Term-Structure Models

We derive an explicit asymptotic approximation for implied volatilities of caplets under the assumption that the short-rate is described by a generic quadratic term-structure model. In addition to providing an asymptotic accuracy result, we perform experiments in order to gauge the numerical accurac

Lab Rats Math 8 Rigor 4 ·  December 8, 2022

Optimal Control of the Ethena Yield-Bearing Stablecoin

We formulate and solve stochastic control problems that model the core yield-generating strategy of the Ethena protocol, a decentralized finance (DeFi) stablecoin that earns yield by combining a long position in staked Ethereum (stETH) with an equal-sized short position in ETH perpetual futures. The

Lab Rats Math 8 Rigor 3 ·  May 11, 2026

Optimal Liquidation of Perpetual Contracts

An agent holds a position in a perpetual contract with payoff function $ψ$ and attempts to liquidate the position while managing transaction costs, inventory risk, and funding rate payments. By solving the agent’s stochastic control problem we obtain a closed-form expression for the optimal trading

Lab Rats Math 8 Rigor 3 ·  January 15, 2026

Short-Rate Derivatives in a Higher-for-Longer Environment

We introduce a class of short-rate models that exhibit a ``higher for longer’’ phenomenon. Specifically, the short-rate is modeled as a general time-homogeneous one-factor Markov diffusion on a finite interval. The lower endpoint is assumed to be regular, exit or natural according to boundary classi

Lab Rats Math 8.5 Rigor 2.5 ·  February 28, 2025

Short-Rate-Dependent Volatility Models

We price European options in a class of models in which the volatility of the underlying risky asset depends on the short rate of interest. Our study results in an explicit pricing formula that depends on knowledge of a characteristic function. We provide examples of models in which the characterist

Lab Rats Math 8 Rigor 2.5 ·  January 31, 2026

Optimal positioning in derivative securities in incomplete markets

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

Lab Rats Math 8.5 Rigor 2 ·  February 29, 2024

Interest rate derivatives in a CTMC setting: pricing, replication and Ross recovery

We consider a financial market in which the short rate is modeled by a continuous time Markov chain (CTMC) with a finite state space. In this setting, we show how to price any financial derivative whose payoff is a function of the state of the underlying CTMC at the maturity date. We also show how t

Lab Rats Math 6.5 Rigor 1.5 ·  September 21, 2024

A Calculus of Variations Approach to Stochastic Control

We use classical tools from calculus of variations to formally derive necessary conditions for a Markov control to be optimal in a standard finite time horizon stochastic control problem. As an example, we solve the well-known Merton portfolio optimization problem.

Lab Rats Math 6.5 Rigor 1 ·  September 1, 2025

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