56 research outputs found
Combining losing games into a winning game
Parrondo's paradox is extended to regime switching random walks in random
environments. The paradoxical behavior of the resulting random walk is
explained by the effect of the random environment. Full characterization of the
asymptotic behavior is achieved in terms of the dimensions of some random
subspaces occurring in Oseledec's theorem. The regime switching mechanism gives
our models a richer and more complex asymptotic behavior than the simple random
walks in random environments appearing in the literature, in terms of
transience and recurrence
Optimal hedging in discrete time
Building on the work of Schweizer (1995) and Cern and Kallseny (2007), we
present discrete time formulas minimizing the mean square hedging error for
multidimensional assets. In particular, we give explicit formulas when a
regime-switching random walk or a GARCH-type process is utilized to model the
returns. Monte Carlo simulations are used to compare the optimal and delta
hedging methods.Comment: Cette pr\'epublication appara\^it aussi sur SSRN et les cahiers du
GERA
Central limit theorems for martingales-I : continuous limits
When the limiting compensator of a sequence of martingales is continuous, we
obtain a weak convergence theorem for the martingales; the limiting process can
be written as a Brownian motion evaluated at the compensator and we find
sufficient conditions for both processes to be independent. Examples of
applications are provided, notably for occupation time processes and
statistical estimators of financial volatility measures
Multivariate Hawkes-based Models in LOB: European, Spread and Basket Option Pricing
In this paper, we consider pricing of European options and spread options for
Hawkes-based model for the limit order book. We introduce multivariate Hawkes
process and the multivariable general compound Hawkes process. Exponential
multivariate general compound Hawkes processes and limit theorems for them,
namely, LLN and FCLT, are considered then. We also consider a special case of
one-dimensional EMGCHP and its limit theorems. Option pricing with EGCHP
in LOB, hedging strategies, and numerical example are presented. We also
introduce greeks calculations for those models. Margrabe's spread options
valuations with Hawkes-based models for two assets and numerical example are
presented. Also, Margrabe's spread option pricing with two EMGCHP and
numerical example are included. Basket options valuations with numerical
example are included. We finally discuss the implied volatility and implied
order flow. It reveals the relationship between stock volatility and the order
flow in the limit order book system. In this way, the Hawkes-based model can
provide more market forecast information than the classical Black-Scholes
model
MONTE CARLO APPROXIMATIONS OF AMERICAN OPTIONS THAT PRESERVE MONOTONICITY AND CONVEXITY
Numerical Methods in Finance, Springer Proceedings in Mathematics, 2011.International audienceIt can be shown that when the payoff function is convex and decreasing (re- spectively increasing) with respect to the underlying (multidimensional) assets, then the same is true for the value of the associated American option, provided some conditions are satisfied. In such a case, all Monte Carlo methods proposed so far in the literature do not preserve the convexity or monotonicity properties. In this paper, we propose a method of approximation for American options which can preserve both convexity and monotonicity. The resulting values can then be used to define exercise times and can also be used in combination with primal-dual methods to get sharper bounds. Other application of the algorithm include finding optimal hedging strategies
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