Search results for "Complete market"
showing 10 items of 13 documents
Value preserving portfolio strategies and the minimal martingale measure
1998
We consider some relations between the minimal martingale measure and the value preserving martingale measure in a continuous-time securities market. Under the assumption of continuous share prices we show that under a structure condition both these martingale measures exist and indeed coincide. This however does not mean that the corresponding concepts of value preserving portfolio strategies and (local) risk minimisation in the area of option hedging in incomplete markets are identical.
Pricing the Option to Surrender in Incomplete Markets
2010
New international accounting standards require insurers to reflect the value of embedded options and guarantees in their products. Pricing techniques based on the Black and Scholes paradigm are often used; however, the hypotheses underneath this model are rarely met. We propose a framework that encompasses the most known sources of incompleteness. We show that the surrender option, joined with a wide range of claims embedded in insurance contracts, can be priced through our tool, and deliver hedging portfolios to mitigate the risk arising from their positions. We provide extensive empirical analysis to highlight the effect of incompleteness on the fair value of the option.
Pricing of forwards and other derivatives in cointegrated commodity markets
2015
Abstract We analyze cointegration in commodity markets, and propose a parametric class of pricing measures which preserves cointegration for forward prices with fixed time to maturity. We present explicit expressions for the term structure of volatility and correlation in the context of our spot price models based on continuous-time autoregressive moving average dynamics for the stationary components. The term structures have many interesting shapes, and we provide some empirical evidence from refined oil future prices at NYMEX defending our modeling idea. Motivated from these results, we present a cointegrated forward price dynamics using the Heath–Jarrow–Morton approach. In this setting, …
Liquidity and dirty hedging in the Nordic electricity market
2012
Abstract Hedging involves tradeoffs in incomplete markets because the number of hedging instruments is limited. Even when an extensive set of hedging instruments is available, the ease with which these instruments can be traded may be highly variable. This study finds systematic variations in liquidity in different segments of the Nordic electricity swap market and analyzes the potential for replacing low-liquidity, delivery-period-matched hedging instruments with more liquid, delivery-period-mismatched hedging instruments. When the costs of implementing such dirty hedging strategies are lower than those of the replaced hedging instruments and the loss of hedge effectiveness is small, dirty…
Unawareness and bankruptcy: A general equilibrium model
1998
International audience; We present a consistent pure-exchange general equilibrium model where agents may not be able to foresee all possible future contingencies. In this context, even with nominal assets and complete asset markets, an equilibrium may not exist without appropriate assumptions. Specific examples are provided. An existence result is proved under the main assumption that there are sufficiently many states that all the agents foresee. An intrinsic feature of the model is bankruptcy, which agents may involuntarily experience in the unforeseen states.
Pricing and hedging GDP-linked bonds in incomplete markets
2018
Abstract We model the super-replication of payoffs linked to a country’s GDP as a stochastic linear program on a discrete time and state-space scenario tree to price GDP-linked bonds. As a byproduct of the model we obtain a hedging portfolio. Using linear programming duality we compute also the risk premium. The model applies to coupon-indexed and principal-indexed bonds, and allows the analysis of bonds with different design parameters (coupon, target GDP growth rate, and maturity). We calibrate for UK and US instruments, and carry out sensitivity analysis of prices and risk premia to the risk factors and bond design parameters. We also compare coupon-indexed and principal-indexed bonds. F…
Pricing and Hedging GDP-Linked Bonds in Incomplete Markets
2017
We model the super-replication of payoffs linked to a country's GDP as a stochastic linear program on a discrete time and state-space scenario tree to price GDP-linked bonds. As a byproduct of the model, we obtain a hedging portfolio. Using linear programming duality we also compute the risk premium. The model applies to coupon-indexed and principal-indexed bonds, and allows the analysis of bonds with different design parameters (coupon, target GDP growth rate, and maturity). We calibrate for UK and US instruments and carry out a sensitivity analysis of prices and risk premia to the risk factors and bond design parameters. We also compare coupon-indexed and principal-indexed bonds. Results …
The prometeia model for managing insurance policies with guarantees
2008
Publisher Summary This chapter discusses the development of a scenario-based optimization model for asset and liability management for the participating policies with guarantees and bonus provisions offered by Italian insurers. The changing landscape of the financial services in Italy sets the backdrop for the development of this system which was the result of a multi-year collaborative effort between academic researchers, the research staff at Prometeia in Bologna, and end-users from diverse Italian insurers. It also presents and discusses the model and its key feature, and introduces several extensions. The resulting system allows the analysis of the tradeoffs facing an insurance firm in …
A parsimonious model for generating arbitrage-free scenario trees
2016
Simulation models of economic, financial and business risk factors are widely used to assess risks and support decision-making. Extensive literature on scenario generation methods aims at describing some underlying stochastic processes with the least number of scenarios to overcome the ‘curse of dimensionality’. There is, however, an important requirement that is usually overlooked when one departs from the application domain of security pricing: the no-arbitrage condition. We formulate a moment matching model to generate multi-factor scenario trees for stochastic optimization satisfying no-arbitrage restrictions with a minimal number of scenarios and without any distributional assumptions.…
Generating Multi-Asset Arbitrage-Free Scenario Trees with Global Optimization
2013
Simulation models of economic, financial and business risk factors are widely used to assess risks and support decision-making. Extensive literature on scenario generation methods aims at describing some underlying stochastic processes with the least number of scenarios to overcome the "curse of dimensionality". There is, however, an important requirement that is usually overlooked when one departs from the application domain of security pricing: the no-arbitrage condition. We formulate a moment matching model to generate multi-factor scenario trees satisfying no-arbitrage restrictions with a minimal number of scenarios and without any distributional assumptions. The resulting global optimi…