Fundamental theorem of asset pricing with acceptable risk in markets with frictions

Option Pricing in an Imperfect World

In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage property. We show that prices are coherent if and only if the set of pricing measures is non empty, i.e. if pricing by expectation is possible. We then obtain a decomposition of coherent prices highlighting the role of bubbles. eventually we show that under very weak conditions the coherent pricing of options allows for a very clear representation from which it …

Pointwise Arbitrage Pricing Theory in Discrete Time

We develop a robust framework for pricing and hedging of derivative securities in discrete-time financial markets. We consider markets with both dynamically and statically traded assets and make minimal measurability assumptions. We obtain an abstract (pointwise) Fundamental Theorem of Asset Pricing and Pricing--Hedging Duality. Our results are general and in particular include so-called model independent results of Acciao et al. (2016), Burzoni et al. (2016) as well as seminal results of Dalang et al. (1990) in a classical probabilistic approach. Our analysis is scenario--based: a model speci…

随机波动率下期权定价关于混合解的闭式近似

Closed-form approximations with respect to the mixing solution for option pricing under stochastic volatility

针对带时变参数的Heston和GARCH diffusion随机波动率模型下的欧式看跌期权定价，提出基于Black-Scholes公式期望与二阶泰勒展开的闭式近似方法，推导定价公式与余项界，验证了误差在应用可接受范围内。

Option Pricing in Illiquid Markets with Jumps

The classical linear Black--Scholes model for pricing derivative securities is a popular model in financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the assumption on the underlying asset price dynamics following a geometric Brownian motion. The main purpose of this paper is to generalize the classical Black--Scholes model for pricing derivative securities by taking into account feedback effects due to an influence of a large trader on the underlying asset price dynamics exhibiting random jumps. The assumption that a…

从衍生品定价角度审视常产品市场制造者中的流动性代币

A Derivative Pricing Perspective on Liquidity Tokens in Constant Product Market Makers

本文从衍生品定价角度探讨了常产品市场制造者中流动性代币的定价与对冲问题，提出新的定价公式以改进流动性代币的估值方法。

Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costs

In discrete time markets with proportional transaction costs, Schachermayer (2004) shows that robust no-arbitrage is equivalent to the existence of a strictly consistent price system. In this paper, we introduce the concept of prospective strict no-arbitrage that is a variant of the strict no-arbitrage property from Kabanov, Rásonyi, and Stricker (2002). The prospective strict no-arbitrage condition is slightly weaker than robust no-arbitrage, and it implies that the set of portfolios attainable from zero initial endowment is closed in probability. A weak version of prospective strict no-arbit…

Asset Pricing with General Transaction Costs: Theory and Numerics

We study risk-sharing equilibria with general convex costs on the agents' trading rates. For an infinite-horizon model with linear state dynamics and exogenous volatilities, we prove that the equilibrium returns mean-revert around their frictionless counterparts - the deviation has Ornstein-Uhlenbeck dynamics for quadratic costs whereas it follows a doubly-reflected Brownian motion if costs are proportional. More general models with arbitrary state dynamics and endogenous volatilities lead to multidimensional systems of nonlinear, fully-coupled forward-backward SDEs. These fall outside the sco…

Risk measures beyond frictionless markets

We develop a general theory of risk measures that determines the optimal amount of capital to raise and invest in a portfolio of reference traded securities in order to meet a pre-specified regulatory requirement. The distinguishing feature of our approach is that we embed portfolio constraints and transaction costs into the securities market. As a consequence, we have to dispense with the property of translation invariance, which plays a key role in the classical theory. We provide a comprehensive analysis of relevant properties such as star shapedness, positive homogeneity, convexity, quasic…

跳跃扩散模型中的过滤约简与完备性

Filtration Reduction and Completeness in Jump-Diffusion Models

本文研究不完备跳跃扩散市场中的衍生品定价与对冲，提出通过过滤约简构造虚构完备市场以获得唯一等价鞅测度，并利用一致性概念将其提升回原始经济，从简单设定逐步推广到一般模型。

Optimal measure preserving derivatives revisited

This article clarifies the relationship between pricing kernel monotonicity and the existence of opportunities for stochastic arbitrage in a complete and frictionless market of derivative securities written on a market portfolio. The relationship depends on whether the payoff distribution of the market portfolio satisfies a technical condition called adequacy, meaning that it is atomless or is comprised of finitely many equally probable atoms. Under adequacy, pricing kernel nonmonotonicity is equivalent to the existence of a strong form of stochastic arbitrage involving distributional replicat…

Disentangling Price, Risk and Model Risk: V&R measures

We propose a method to assess the intrinsic risk carried by a financial position $X$ when the agent faces uncertainty about the pricing rule assigning its present value. Our approach is inspired by a new interpretation of the quasiconvex duality in a Knightian setting, where a family of probability measures replaces the single reference probability and is then applied to value financial positions. Diametrically, our construction of Value\&Risk measures is based on the selection of a basket of claims to test the reliability of models. We compare a random payoff $X$ with a given class of derivat…

A Mean-Field Game Approach to Equilibrium Pricing in Solar Renewable Energy Certificate Markets

Solar Renewable Energy Certificate (SREC) markets are a market-based system that incentivizes solar energy generation. A regulatory body imposes a lower bound on the amount of energy each regulated firm must generate via solar means, providing them with a tradeable certificate for each MWh generated. Firms seek to navigate the market optimally by modulating their SREC generation and trading rates. As such, the SREC market can be viewed as a stochastic game, where agents interact through the SREC price. We study this stochastic game by solving the mean-field game (MFG) limit with sub-population…

Optimal Investment, Demand and Arbitrage under Price Impact

This paper studies the optimal investment problem with random endowment in an inventory-based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules and demand schedules for contingent claims. For exponential market makers preferences, we establish two effects due to price impact: constrained trading, and non-linear hedging costs. To the former, wealth processes in the impact model are identified with those in a model without impact, but with constrained trading, where the (random) constraint set is gen…