On Equilibrium Prices in Continuous Time

The impact of startup costs and the grid operator on the power price equilibrium

In this paper we propose a quadratic programming model that can be used for calculating the term structure of electricity prices while explicitly modeling startup costs of power plants. In contrast to other approaches presented in the literature, we incorporate the startup costs in a mathematically rigorous manner without relying on ad hoc heuristics. Moreover, we propose a tractable approach for estimating the startup costs of power plants based on their historical production. Through numerical simulations applied to the entire UK power grid, we demonstrate that the inclusion of startup costs…

Hedging in an equilibrium-based model for a large investor

We study a financial model with a non-trivial price impact effect. In this model we consider the interaction of a large investor trading in an illiquid security, and a market maker who is quoting prices for this security. We assume that the market maker quotes the prices such that by taking the other side of the investor's demand, the market maker will arrive at maturity with maximal expected wealth. Within this model we concentrate on the issue of contingent claims' hedging.

Model-free trading and hedging with continuous price paths

In this paper, we provide a model-independent extension of the paradigm of dynamic hedging of derivative claims. We relate model-independent replication strategies to local martingales having a closed form which we can characterise via solutions of coupled PDEs. We provide a general framework and then apply it to a market with no traded claims, a market with an underlying asset and a convex claim and a market with an underlying asset and a set of co-maturing call options. The results encompass known examples of model-independent identities and provide a methodology for deriving new identities.

Kyle's Model with Stochastic Liquidity

We construct an equilibrium for the continuous time Kyle's model with stochastic liquidity, a general distribution of the fundamental price, and correlated stock and volatility dynamics. For distributions with positive support, our equilibrium allows us to study the impact of the stochastic volatility of noise trading on the volatility of the asset. In particular, when the fundamental price is log-normally distributed, informed trading forces the log-return up to maturity to be Gaussian for any choice of noise-trading volatility even though the price process itself comes with stochastic volati…

Price formation and optimal trading in intraday electricity markets

We develop a tractable equilibrium model for price formation in intraday electricity markets in the presence of intermittent renewable generation. Using stochastic control theory, we identify the optimal strategies of agents with market impact and exhibit the Nash equilibrium in closed form for a finite number of agents as well as in the asymptotic framework of mean field games. Our model reproduces the empirical features of intraday market prices, such as increasing price volatility at the approach of the delivery date and the correlation between price and renewable infeed forecasts, and rela…

Discrete Time vs Continuous Time Stock-price Dynamics and implications for Option Pricing

In the present paper we construct stock price processes with the same marginal log-normal law as that of a geometric Brownian motion and also with the same transition density (and returns' distributions) between any two instants in a given discrete-time grid. We then illustrate how option prices based on such processes differ from Black and Scholes', in that option prices can be either arbitrarily close to the option intrinsic value or arbitrarily close to the underlying stock price. We also explain that this is due to the particular way one models the stock-price process in between the grid t…

Continuous-time Duality for Super-replication with Transient Price Impact

We establish a super-replication duality in a continuous-time financial model where an investor's trades adversely affect bid- and ask-prices for a risky asset and where market resilience drives the resulting spread back towards zero at an exponential rate. Similar to the literature on models with a constant spread, our dual description of super-replication prices involves the construction of suitable absolutely continuous measures with martingales close to the unaffected reference price. A novel feature in our duality is a liquidity weighted $L^2$-norm that enters as a measurement of this clo…

Default and Systemic Risk in Equilibrium

We develop a finite horizon continuous time market model, where risk averse investors maximize utility from terminal wealth by dynamically investing in a risk-free money market account, a stock written on a default-free dividend process, and a defaultable bond, whose prices are determined via equilibrium. We analyze financial contagion arising endogenously between the stock and the defaultable bond via the interplay between equilibrium behavior of investors, risk preferences and cyclicality properties of the default intensity. We find that the equilibrium price of the stock experiences a jump …

是否产生泡沫：OLG经济中的资产价格动态与最优性

To Bubble or Not to Bubble: Asset Price Dynamics and Optimality in OLG Economies

该研究针对带分红资产的OLG交换经济，推导了泡沫均衡存在条件与帕累托最优条件，探究了资产价格动态和均衡最优性的关联。