Options & Derivatives Pricing

In this paper we study the pricing and hedging of nonreplicable contingent claims, such as long-term insurance contracts like variable annuities. Our approach is based on the benchmark-neutral pricing framework of Platen (2024), which differs from the classical benchmark approach by using the stock

This work analytically characterizes impermanent loss for automated market makers (AMMs) in decentralized markets such as Uniswap or Balancer (CPMM). We derive a static replication formula for the pool’s value using a combination of European calls and puts. Furthermore, we establish a result guarant

As automated trading gains traction in the financial market, algorithmic investment strategies are increasingly prominent. While Large Language Models (LLMs) and Agent-based models exhibit promising potential in real-time market analysis and trading decisions, they still experience a significant -20

In this paper, we establish existence, uniqueness, and regularity properties of the solutions to multi-dimensional backward stochastic Volterra integral equations (BSVIEs), whose (possibly random) generator reflects nonlinear dependence on both the solution process and the martingale integrand compo

It is a challenge to estimate fund performance by compounded returns. Arguably, it is incorrect to use yearly returns directly for compounding, with reported annualized return of above 60% for Medallion for the 31 years up to 2018. We propose an estimation based on fund sizes and trading profits and

This paper investigates the consumption and investment decisions of an individual facing uncertain lifespan and stochastic labor income within a Black-Scholes market framework. A key aspect of our study involves the agent’s option to choose when to acquire life insurance for bequest purposes. We exa

We study an optimal stopping problem with an unbounded, time-dependent and discontinuous reward function. This problem is motivated by the pricing of a variable annuity contract with guaranteed minimum maturity benefit, under the assumption that the policyholder’s surrender behaviour maximizes the r

We introduce the notions of Collective Arbitrage and of Collective Super-replication in a discrete-time setting where agents are investing in their markets and are allowed to cooperate through exchanges. We accordingly establish versions of the fundamental theorem of asset pricing and of the pricing

This paper concerns a local volatility model in which volatility takes two possible values, and the specific value depends on whether the underlying price is above or below a given threshold value. The model is known, and a number of results have been obtained for it. In particular, option pricing f

Using the option delta systematically, we derive tighter lower and upper bounds of the Black-Scholes implied volatility than those in Tehranchi [SIAM J. Financ. Math. 7 (2016), 893-916]. As an application, we propose a Newton-Raphson algorithm on the log price that converges rapidly for all price ra

Automated Market Makers (AMMs) are a class of smart contracts on Ethereum and other blockchains that “make markets” autonomously. In other words, AMMs stand ready to trade with other market participants that interact with them, at the conditions determined by the AMM. In this this paper, which relie

The classical Merton investment problem predicts deterministic, state-dependent portfolio rules; however, laboratory and field evidence suggests that individuals often prefer randomized decisions leading to stochastic and noisy choices. Fudenberg et al. (2015) develop the additive perturbed utility

We study non-linear Backward Stochastic Differential Equations (BSDEs) driven by a Brownian motion and p default martingales. The driver of the BSDE with multiple default jumps can take a generalized form involving an optional finite variation process. We first show existence and uniqueness. We then

In this work, we introduce amortizing perpetual options (AmPOs), a fungible variant of continuous-installment options suitable for exchange-based trading. Traditional installment options lapse when holders cease their payments, destroying fungibility across units of notional. AmPOs replace explicit

This paper builds on “Collective Arbitrage and the Value of Cooperation” by Biagini et al. (2025, forthcoming in “Finance and Stochastics”), which introduced in discrete time the notions of collective arbitrage and super-replication in a multi-agent market framework, where agents may operate in seve

In this paper, we consider scaling limits of exponential utility indifference prices for European contingent claims in the Bachelier model. We show that the scaling limit can be represented in terms of the \emph{specific relative entropy}, and in addition we construct asymptotic optimal hedging stra

We consider a continuous-time financial market with an asset whose price is modeled by a linear stochastic differential equation with drift and volatility switching driven by a uniformly ergodic jump Markov process with a countable state space (in fact, this is a Black-Scholes model with Markov swit

This paper is devoted to obtain closed form solutions for the semiclassical (or WKB) approximation of the heat kernel propagator of the diffusion equation defined by the constant elasticity variance (CEV) option pricing model. One of the key points is that our calculations are based on the Van Vleck

In this study, we consider the asset pricing under model uncertainty with discrete time and states structure. For the single-period securities model, we give a novel definition of arbitrage under a family of probability, and explore of its relationship with risk neutral probability measure. Focusing

We expose a theoretical hedging optimization framework with variational preferences under convex risk measures. We explore a general dual representation for the composition between risk measures and utilities. We study the properties of the optimization problem as a convex and monotone map per se. W