• Management Science and Financial Engineering
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• v.19 no.2
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• pp.37-42
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• 2013

This paper suggests a numerical method for valuation of European and American options under the two L$\acute{e}$vy Processes, Normal Inverse Gaussian Model and the Variance Gamma model. The method is based on approximation of underlying asset price using a finite-state, time-homogeneous Markov chain. We examine the effectiveness of the proposed method with simulation results, which are compared with those from the existing numerical method, the lattice-based method.

• Journal of Korean Institute of Industrial Engineers
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• v.38 no.4
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• pp.249-253
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• 2012

This paper suggests a numerical method for valuation of American options under the Kou model (double exponential jump diffusion model). The method is based on approximation of underlying asset price using a finite-state, time-homogeneous Markov chain. We examine the effectiveness of the proposed method with simulation results, which are compared with those from the conventional numerical method, the finite difference method for PIDE (partial integro-differential equation).

• Korean Journal of Mathematics
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• v.25 no.2
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• pp.229-246
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• 2017

This paper concerns barrier option of American type where the underlying price is monitored during only part of the option's life. Analytic valuation formulas of the American partial barrier options are obtained by approximation method. This approximation method is based on barrier options along with exponential early exercise policies. This result is an extension of Jun and Ku [10] where the exercise policies are constant.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.2
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• pp.151-160
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• 2011

Typically, it is hard to find a closed form solution of option pricing formula under an asset governed by a change point process. In this paper we derive a closed-form solution of the valuation function for an American perpetual put option under an asset having a change point. Structural changes are formulated through a change-point process with a Markov chain. The modified smooth-fit technique is used to obtain the closed-form valuation function. We also guarantee the optimality of the solution via the proof of a corresponding verification theorem. Numerical examples are included to illustrate the results.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.745-751
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• 2002

In this paper, we Shall find the unique rational price associated with the exchange option. Also, we find the decomposition of Snell envelope and value function of the American exchange option.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.519-536
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• 2005

The purpose of this paper is to propose several approximating methods to obtain the American option prices under jump-diffusion processes. The first method is to extend an approximating method to the optimal exercise boundary by a multipiece exponential function suggested by Ju [17]. The second approach is to modify the analytical methods of MacMillan [20] and Zhang [25] in a discrete time space. The third approach is to apply the simulation technique of Ibanez and Zapareto [14] to the problem of American option pricing when the jumps are allowed. Finally, we compare the numerical performance of each suggesting method with those of the previous numerical approaches.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.397-406
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• 2013

We present an improved binomial method for pricing European- and American-type Asian options based on the arithmetic average of the prices of the underlying asset. At each node of the tree we propose a simple algorithm to choose the representative averages among all the effective averages. Then the backward valuation process and the interpolation are performed to compute the price of the option. The simulation results for European and American Asian options show that the proposed method gives much more accurate price than other recent lattice methods with less computational effort.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.11-20
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• 2000

This paper presents a formula that relates the optimal exercise boundaries of American call and put options on futures contract. It is shown that the geometric mean of the optimal exercise boundaries for call and put written on the same futures contract with the same exercise price is equal to the exercise price which is time invariant. The paper also investigates the properties of American calls and puts on futures contract.

• Industrial Engineering and Management Systems
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• v.10 no.2
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• pp.170-177
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• 2011

We present an improved binomial method for pricing financial deriva-tives by using cell averages. After non-overlapping cells are introduced around each node in the binomial tree, the proposed method calculates cell averages of payoffs at expiry and then performs the backward valuation process. The price of the derivative and its hedging parameters such as Greeks on the valuation date are then computed using the compact scheme and Richardson extrapolation. The simulation results for European and American barrier options show that the pro-posed method gives much more accurate price and Greeks than other recent lattice methods with less computational effort.

• Journal of Korean Institute of Industrial Engineers
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• v.32 no.3
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• pp.180-190
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• 2006

We evaluate the economic value and the optimal investment timing of IMT-2000 in Korea, in the perspective of a service provider who owns the business license for IMT-2000, by using the real options analysis. The result clearly shows the project value with options is positive and delaying the investment is more favorable to the provider. Binomial lattice approach, in which we try to describe American call option and sequential compound option, and sensitivity analysis present the optimal decisions according to future states and enable the management to make decision strategically and proactively.