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Mathematical Finance's Blog

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LIQUIDITY IN A BINOMIAL MARKET

February 15, 2012 Comments (0)

We study the binomial version of the illiquid market model introduced by Çetin, Jarrow, and Protter for continuous time and develop efficient numerical methods for its analysis. In particular, we characterize the liquidity premium that results from the model. In Çetin, Jarrow, and Protter, the arbitrage free price of a European option traded in this illiquid market is equal to the classical value. However, the corresponding hedge does not exist and the price is obtained only in L2‐approximating...

THE TRACKING ERROR RATE OF THE DELTA‐GAMMA HEDGING STRATEGY

February 15, 2012 Comments (0)

We analyze the convergence rate of the quadratic tracking error, when a Delta‐Gamma hedging strategy is used at N discrete times. The fractional regularity of the payoff function plays a crucial role in the choice of the trading dates, in order to achieve optimal rates of convergence.

SERIES EXPANSION OF THE SABR JOINT DENSITY

February 15, 2012 Comments (0)

Under the SABR stochastic volatility model, pricing and hedging contracts that are sensitive to forward smile risk (e.g., forward starting options, barrier options) require the joint transition density. In this paper, we address this problem by providing closed‐form representations, asymptotically, of the joint transition density. Specifically, we construct an expansion of the joint density through a hierarchy of parabolic equations after applying total volatility‐of‐volatility scaling and a...

BETTER THAN DYNAMIC MEAN‐VARIANCE: TIME INCONSISTENCY AND FREE CASH FLOW STREAM

February 15, 2012 Comments (0)

As the dynamic mean‐variance portfolio selection formulation does not satisfy the principle of optimality of dynamic programming, phenomena of time inconsistency occur, i.e., investors may have incentives to deviate from the precommitted optimal mean‐variance portfolio policy during the investment process under certain circumstances. By introducing the concept of time inconsistency in efficiency and defining the induced trade‐off, we further demonstrate in this paper that investors behave...

SKEWNESS‐AWARE ASSET ALLOCATION: A NEW THEORETICAL FRAMEWORK AND EMPIRICAL EVIDENCE

February 15, 2012 Comments (0)

This paper presents a new measure of skewness, skewness‐aware deviation, that can be linked to prospective satisficing risk measures and tail risk measures such as Value‐at‐Risk. We show that this measure of skewness arises naturally also when one thinks of maximizing the certainty equivalent for an investor with a negative exponential utility function, thus bringing together the mean‐risk, expected utility, and prospective satisficing measures frameworks for an important class of investor...

SCHUR CONVEX FUNCTIONALS: FATOU PROPERTY AND REPRESENTATION

February 15, 2012 Comments (0)

The Fatou property for every Schur convex lower semicontinuous (l.s.c.) functional on a general probability space is established. As a result, the existing quantile representations for Schur convex l.s.c. positively homogeneous convex functionals, established on  for either p= 1 or p=∞ and with the requirement of the Fatou property, are generalized for , with no requirement of the Fatou property. In particular, the existing quantile representations for law invariant coherent risk measures and...