• Industrial Engineering and Management Systems
• /
• v.12 no.2
• /
• pp.85-94
• /
• 2013

This research investigates the supply chain contract between a distributor and a supplier in which the selling period is relatively short in comparison with long production lead time. At the first stage, supplier who is a Stackelberg leader offers the distributor a contract with a set of parameters, and subjected to those parameters, the distributor places the number of initial orders as well as options. In order to purchase the option, the distributor pays non-linear option premium price with respect to the number of purchased options. At the second stage, based on realized demand, the distributor has the right to exercise option as either put or call which is limited up to the number of purchased options. The wholesale price contract is used as a benchmarking contract. This research has confirmed that the supply chain contract with a non-linear option premium price can help to coordinate the supply chain.

• The Korean Journal of Applied Statistics
• /
• v.21 no.5
• /
• pp.755-763
• /
• 2008

This paper approaches the problem of option pricing in an incomplete market, where the underlying asset price process follows a compound Poisson model. We assume that the price process follows a compound Poisson model under an equivalent martingale measure and it converges weakly to the Black-Scholes model. First, we express the option price as the expectation of the discounted payoff and expand it at the Black-Scholes price to obtain a pricing formula with three unknown parameters. Then we estimate those parameters using the market option data. This method can use the option data on the same stock with different expiration dates and different strike prices.

• Journal of the Chungcheong Mathematical Society
• /
• v.33 no.2
• /
• pp.181-195
• /
• 2020

This paper suggests the price of vulnerable European option under a constant elasticity of variance model by using asymptotic analysis technique and obtains the approximated solution of the option price. Finally, we illustrate an accuracy of the vulnerable option price so that the approximate solution is well-defined.

• Journal of applied mathematics & informatics
• /
• v.4 no.2
• /
• pp.379-386
• /
• 1997

This paper considers the price at time zero of a contingent claim when the process is a diffusion/point process model . And we apply this price to European option.

• Journal of the Korean Statistical Society
• /
• v.36 no.2
• /
• pp.237-256
• /
• 2007

This paper studies the problem of option pricing in an incomplete market. The market incompleteness comes from the discontinuity of the underlying asset price process which is, in particular, assumed to be a compound Poisson process. To find a reasonable price for a European contingent claim, we first find the unique minimal martingale measure and get a price by taking an expectation of the payoff under this measure. To get a closed-form price, we use an asymptotic expansion. In case where the minimal martingale measure is a signed measure, we use a sequence of martingale measures (probability measures) that converges to the equivalent martingale measure in the limit to compute the price. Again, we get a closed form of asymptotic option price. It is the Black-Scholes price and a correction term, when the distribution of the return process has nonzero skewness up to the first order.

• The Korean Journal of Applied Statistics
• /
• v.29 no.1
• /
• pp.181-192
• /
• 2016

We consider several methods to approximate option prices with correction terms to the Black-Scholes option price. These methods are able to compute option prices from various risk-neutral distributions using relatively small data and simple computation. In this paper, we compare the performance of Edgeworth expansion, A-type and C-type Gram-Charlier expansions, a method of using Normal inverse gaussian distribution, and an asymptotic method of using nonlinear regression through simulation experiments and real KOSPI200 option data. We assume the variance gamma model in the simulation experiment, which has a closed-form solution for the option price among the pure jump $L{\acute{e}}vy$ processes. As a result, we found that methods to approximate an option price directly from the approximate price formula are better than methods to approximate option prices through the approximate risk-neutral density function. The method to approximate option prices by nonlinear regression showed relatively better performance among those compared.

• The Korean Journal of Applied Statistics
• /
• v.24 no.4
• /
• pp.721-733
• /
• 2011

We consider the state price densities that are implicit in financial asset prices. In the pricing of an option, the state price density is proportional to the second derivative of the option pricing function and this relationship together with no arbitrage principle imposes restrictions on the pricing function such as monotonicity and convexity. Since the state price density is a proper density function and most of the shape constraints are caused by this, we propose to estimate the state price density directly by specifying candidate densities in a flexible nonparametric way and applying methods of regularization under extra constraints. The problem is easy to solve and the resulting state price density estimates satisfy all the restrictions required by economic theory.

• Bulletin of the Korean Mathematical Society
• /
• v.39 no.4
• /
• pp.705-714
• /
• 2002

We consider a jump-diffusion model generated by a Levy process for an asset price. We present an error estimate for the option prices between the jump-diffusion model and the Black-scholes model when the former converges weakly to the latter.

• East Asian mathematical journal
• /
• v.34 no.3
• /
• pp.239-248
• /
• 2018

In this paper, we derive a closed-form formula of a second-order approximation for a European corrected option price under stochastic elasticity of variance model mentioned in Kim et al. (2014) [1] [J.-H. Kim, J Lee, S.-P. Zhu, S.-H. Yu, A multiscale correction to the Black-Scholes formula, Appl. Stoch. Model. Bus. 30 (2014)]. To find the explicit-form correction to the option price, we use Mellin transform approaches.

• Communications for Statistical Applications and Methods
• /
• v.17 no.4
• /
• pp.575-589
• /
• 2010

Exponential L$\acute{e}$evy models have become popular in modeling price processes recently in mathematical finance. Although it is a relatively simple extension of the geometric Brownian motion, it makes the market incomplete so that the option price is not uniquely determined. As a trial to find an appropriate price for an option, we suppose a situation where a hedger wants to initially invest as little as possible, but wants to have the expected squared loss at the end not exceeding a certain constant. For this, we assume that the underlying price process follows a variance-gamma model and it converges to a geometric Brownian motion as its quadratic variation converges to a constant. In the limit, we use the mean-variance approach to find the asymptotic minimum investment with the expected squared loss bounded. Some numerical results are also provided.