Continuous-Time Models for Firm Valuation and Their Collateral Effect on Risk-Neutral Probabilities and No-Arbitraging Principle

Extensions of Merton’s model(EMM)considering the firm’s payments and generating new types of firm value distribution are suggested.In the open log-value/time space,these distributions evolve from initially normal to negatively skewed ones,and their means are concave-down functions of time.When payments are set to zero or proportional to the firm value,EMM turns into the Geometric Brownian model(GBM).We show that risk-neutral probabilities(RNPs)and the no-arbitraging principle(NAP)follow from GBM.When firm’s payments are considered,RNPs and NAP hold for the entire market for short times only,but for long-term investments,RNPs and NAP just temporarily hold for individual stocks as far as mean year returns of the firms issuing those stocks remain constant,and fail when the mean year returns decline.The developed method is applied to firm valuation to derive continuous-time equations for the firm present value and project NPV.

Option Pricing Method in a Market Involving Interval Number Factors

The method for pricing the option in a market with interval number factors is proposed. The no-arbitrage principle in the interval number valued market and the rule to judge the reasonability of a price interval are given. Using the method, the price interval where the riskless interest and the volatility under B-S setting is given. The price interval from binomial tree model when the key factors u, d, R are all interval numbers is also discussed.

Empirical Study on Arbitrage Opportunities in China Copper Futures Market

No-arbitrage bound is established with no-arbitrage theory considering all kinds of trade costs, different deposit and loan interest rate, margin and tax in futures markets. The empirical results find that there are many lower bound arbitrage opportunities in China copper futures market from August 8th, 2003 to August 16th, 2005, Concretely, no-arbitrage opportunity is dominant and lower bound arbitrage is narrow in normal market segment. Lower bound arbitrage almost always exists with huge magnitude in inverted market segment. There is basically no-arbitrage in normal market because spot volume is enough, so that upper or lower bound arbi- trage can be realized, There is mostly lower bound arbitrage in inverted market because spot volume is lack.

An Implicit-Explicit Computational Method Based on Time Semi-Discretization for Pricing Financial Derivatives with Jumps

This paper considers pricing European options under the well-known of SVJ model of Bates and related computational methods. According to the no-arbitrage principle, we first derive a partial differential equation that the value of any European contingent claim should satisfy, where the asset price obeys the SVJ model. This equation is numerically solved by using the implicit- explicit backward difference method and time semi-discretization. In order to explain the validity of our method, the stability of time semi-discretization scheme is also proved. Finally, we use a simulation example to illustrate the efficiency of the method.

An infinite-dimensional model of liquidity in financial markets

We consider a dynamic market model of liquidity where unmatched buy and sell limit orders are stored in order books.The resulting net demand surface constitutes the sole input to the model.We model demand using a two-parameter Brownian motion because(i)different points on the demand curve correspond to orders motivated by different information,and(ii)in general,the market price of risk equation of no-arbitrage theory has no solutions when the demand curve is driven by a finite number of factors,thus allowing for arbitrage.We prove that if the driving noise is infinite-dimensional,then there is no arbitrage in the model.Under the equivalent martingale measure,the clearing price is a martingale,and options can be priced under the no-arbitrage hypothesis.We consider several parameterizations of the model and show advantages of specifying the demand curve as a quantity that is a function of price,as opposed to price as a function of quantity.An online appendix presents a basic empirical analysis of the model:calibration using information from actual order books,computation of option prices using Monte Carlo simulations,and comparison with observed data.

On the Consistency of Option Pricing Model with a General Equilibrium Framework

There are two methods on option pricing, no-arbitrage and equilibrium analysis. We construct a simple economy with continuous consumption, in which we “endogenize” the stochastic process of prices in the option pricing model based on no-arbitrage analysis. With constant relative risk aversion type utility function assumption, we present Merton （1973） option pricing model and find the consistency of the model with a general equilibrium framework. We extend the model to the market with m securities and it turns out similar results.