Pricing American-Style Derivatives with European Call Options

Laprise, Scott B.; Fu, Michael C.; Marcus, Solomon; Lim, Andrew; Zhang, Huiju

doi:10.1287/mnsc.1050.0447

Cited by 22 publications

(20 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, the methodology developed here should also be applicable in other contexts beyond option pricing, e.g., interest rate derivatives. Pathdependent options present another challenge, and future research could tackle barrier options extending ideas from Li and Zhao (2009) to multinomial lattices and American-style options along the lines of Laprise et al (2006). Finally, using the model for hedging is clearly an important practical topic worthy of further investigation.…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

Option Pricing for a Jump-Diffusion Model with General Discrete Jump-Size Distributions

et al. 2017

Management Science

Self Cite

View full text Add to dashboard Cite

W e obtain a closed-form solution for pricing European options under a general jump-diffusion model that can incorporate arbitrary discrete jump-size distributions, including nonparametric distributions such as an empirical distribution. The flexibility in the jump-size distribution allows the model to better capture leptokurtic features found in real-world data. The model uses a discrete-time framework and leads to a pricing formula that is provably convergent to the continuous-time price as the discretization is increased. The solution is easy to implement with fast convergence properties. Numerical results illustrate the efficiency and accuracy of the proposed model and highlight its robustness and flexibility.

show abstract

Section: Conclusion and Future Researchmentioning

confidence: 99%

Option Pricing for a Jump-Diffusion Model with General Discrete Jump-Size Distributions

et al. 2017

Management Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…While numerical solutions have received less attention in the finance literature, a number of approaches have been proposed. Lindset (2007) and Laprise, Fu, Marcus, Lim, and Zhang (2006) use Bermudian options and an interpolation scheme to approximate American values. Bates (1996) and Guo and Huang (2007) extend the quadratic approximation of Barone-Adesi and Whaley (1987) to accommodate the early exercise feature of American options.…”

Section: Introductionmentioning

confidence: 99%

“…Modified binomial and trinomial lattices have been used by Amin (1993), Das and Foresi (1996), Hilliard and Schwartz (2005), and Beliaeva and Nawalkha (2012). Lindset (2007) and Laprise, Fu, Marcus, Lim, and Zhang (2006) use Bermudian options and an interpolation scheme to approximate American values. The papers also focus on different underlyings.…”

Section: Introductionmentioning

confidence: 99%

Using Multivariate Densities to Assign Lattice Probabilities When There Are Jumps

Hilliard

2014

Journal of Futures Markets

View full text Add to dashboard Cite

The lattice approximation to a continuous time process is an especially useful way to value American and real options. We choose lattice probabilities by extending density matching for diffusions to density matching for jump diffusions. Technically, this requires that diffusion and jump components be cast as independent state variables. In this setup, the diffusion probabilities are locally normal and the jump probabilities are locally a mixture of distributions. The lattice is structurally uniform and density matching ensures that all probabilities are legitimate without requiring jumps to non‐adjacent nodes. The approach generalizes easily to several state variables, does not require node adjustments, and does not appear to be dominated by more specialized numerical algorithms. We demonstrate the model for scenarios where the option may depend on a jump diffusion with possible stochastic interest rates and convenience yields. © 2014 Wiley Periodicals, Inc. Jrl Fut Mark 35:385–398, 2015

show abstract

“…American call-on-max or American puton-max options of dividend paying assets, where the underlying assets follows geometric Brownian motions, the value of an American option possesses convexity or monotonicity properties, the Monte Carlo methods described above do not preserve these properties. For a related work, see Laprise et al (2006).…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo Approximations of American Options that Preserve Monotonicity and Convexity

Moral

Rémillard

Rubenthaler³

2012

Springer Proceedings in Mathematics

View full text Add to dashboard Cite

It can be shown that when the payoff function is convex and decreasing (respectively 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. Recently, two-stage Monte Carlo methods were developed by Rogers (2002), Andersen and Broadie (2004) and Haugh and Kogan (2004). For an interesting review of Monte Carlo methods, see Fu et al. (2001).

show abstract

Pricing American-Style Derivatives with European Call Options

Abstract: doi 10.1287/mnsc.1050.044

Cited by 22 publications

References 20 publications

Option Pricing for a Jump-Diffusion Model with General Discrete Jump-Size Distributions

Option Pricing for a Jump-Diffusion Model with General Discrete Jump-Size Distributions

Using Multivariate Densities to Assign Lattice Probabilities When There Are Jumps

Monte Carlo Approximations of American Options that Preserve Monotonicity and Convexity

Contact Info

Product

Resources

About