possible to improve the numerical accuracy of the
Monte Carlo technique applied in this context. Another interesting result in the context of the geometric
Brownian motion converts barrier options into a non path-dependent European option, implying a better
performance of the Monte Carlo method.
SELECTED READING:
Buchen P. and Konstandatos, O. (2005), “A new method of pricing lookback options”, Mathematical Finance,
15, 2, pp 245-259.
Applied Mathematical Finance, pp 173-209.
Carr P. (1995), “Two Extensions to Barrier Option Valuation,”
Merton R.C. (1973), "Theory of Rational option pricing,” The Bell Journal of Economics and Management
Science, 4, pp 141-183.
Gobet E. (2000), “Weak approximation of killed diffusions using Euler schemes”, Stochastic Processes and
their Applications, 87, pp 167-197. (More technical reference)
DATA SOURCE: No data required
NO ARBITRAGE VALUATION OF ASIAN OPTIONS
ISSUES:
The payoff of an Asian option is determined by the average price of the underlying asset up to maturity. No
explicit solution is available. The PDE characterizing the option value is degenerate and requires an
augmentation of the number of state variables. In the context of the geometric Brownian motion, an
interesting reduction of this PDE was obtained in the literature. For general models, the Monte Carlo 英语论文网 【http://www.51lunwen.org】R>simulation technique is the most used methods. The accuracy of these methods is improved by convenient
tricks…
SELECTED READING:
Rogers L.C.G. and Shi Z. (1995), “The value of an Asian option”, Jourmal of Applied Probability, 32, 4, pp
1077-1088.
Lapeyre B. and Temam E. P. (2001), “Competitive Monte Carlo methods for the pricing of Asian options,”
Journal of Computational Finance, 5, 1, pp 39-59.
Vecer, J. (2001): "A new PDE approach for pricing arithmetic average Asian options", Journal of
Computational Finance, 4, 4, 105-113.
DATA SOURCE: No data required
HEDGING UNDER PORTFOLIO CONSTRAINTS
ISSUES:
In the basic Black-Scholes model for options hedging, no constraints are placed on the position in the
underlying security. In order to better fit to real financial markets, an important part of the literature examined
the problem of super-hedging under portfolio constraints, and under gamma constraints. In the context of the
geometric Brownian motion, the value of super-hedging together with the corresponding hedging strategies
have been derived in explicit form. Such hedging strategies imply a bound on the discrete-time hedging error.
SELECTED READING:
Broadie M. Cvitanic J. and Soner M. (1995), “Optimal replication of contingent claims under portfolio
constraints”, The Rev
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