1,887 research outputs found
Hedging with transient price impact for non-covered and covered options
We solve the superhedging problem for European options in a market with
finite liquidity where trading has transient impact on prices, and possibly a
permanent one in addition. Impact is multiplicative to ensure positive asset
prices. Hedges and option prices depend on the physical and cash delivery
specifications of the option settlement. For non-covered options, where impact
at the inception and maturity dates matters, we characterize the superhedging
price as a viscosity solution of a degenerate semilinear pde that can have
gradient constraints. The non-linearity of the pde is governed by the transient
nature of impact through a resilience function. For covered options, the
pricing pde involves gamma constraints but is not affected by transience of
impact. We use stochastic target techniques and geometric dynamic programming
in reduced coordinates
Local time and the pricing of time-dependent barrier options
A time-dependent double-barrier option is a derivative security that delivers
the terminal value at expiry if neither of the continuous
time-dependent barriers b_\pm:[0,T]\to \RR_+ have been hit during the time
interval . Using a probabilistic approach we obtain a decomposition of
the barrier option price into the corresponding European option price minus the
barrier premium for a wide class of payoff functions , barrier functions
and linear diffusions . We show that the barrier
premium can be expressed as a sum of integrals along the barriers of
the option's deltas \Delta_\pm:[0,T]\to\RR at the barriers and that the pair
of functions solves a system of Volterra integral
equations of the first kind. We find a semi-analytic solution for this system
in the case of constant double barriers and briefly discus a numerical
algorithm for the time-dependent case.Comment: 32 pages, to appear in Finance and Stochastic
Option pricing and perfect hedging on correlated stocks
We develop a theory for option pricing with perfect hedging in an inefficient
market model where the underlying price variations are autocorrelated over a
time tau. This is accomplished by assuming that the underlying noise in the
system is derived by an Ornstein-Uhlenbeck, rather than from a Wiener process.
With a modified portfolio consisting in calls, secondary calls and bonds we
achieve a riskless strategy which results in a closed expression for the
European call price which is always lower than Black-Scholes price. We also
obtain a partial differential equation for the option price and study the
sensitivity to several parameters and the risk of the dynamics of the call
price.Comment: 36 pages, 8 figures, 2 table
The effect of non-ideal market conditions on option pricing
Option pricing is mainly based on ideal market conditions which are well
represented by the Geometric Brownian Motion (GBM) as market model. We study
the effect of non-ideal market conditions on the price of the option. We focus
our attention on two crucial aspects appearing in real markets: The influence
of heavy tails and the effect of colored noise. We will see that both effects
have opposite consequences on option pricing.Comment: 26 pages and 8 colored figures. Invited Talk in "Horizons in complex
systems", Messina, 5-8 December 2001. To appear in Physica-
European Option Pricing with Liquidity Shocks
We study the valuation and hedging problem of European options in a market
subject to liquidity shocks. Working within a Markovian regime-switching
setting, we model illiquidity as the inability to trade. To isolate the impact
of such liquidity constraints, we focus on the case where the market is
completely static in the illiquid regime. We then consider derivative pricing
using either equivalent martingale measures or exponential indifference
mechanisms. Our main results concern the analysis of the semi-linear coupled
HJB equation satisfied by the indifference price, as well as its asymptotics
when the probability of a liquidity shock is small. We then present several
numerical studies of the liquidity risk premia obtained in our models leading
to practical guidelines on how to adjust for liquidity risk in option valuation
and hedging.Comment: 25 pages, 6 figure
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