scholarly journals PENENTUAN HARGA OPSI BELI TIPE ASIA DENGAN METODE MONTE CARLO-CONTROL VARIATE

2017 ◽  
Vol 6 (1) ◽  
pp. 29
Author(s):  
NI NYOMAN AYU ARTANADI ◽  
KOMANG DHARMAWAN ◽  
KETUT JAYANEGARA
Keyword(s):  
Monte Carlo ◽  
Standard Error ◽  
Asset Price ◽  
Option Price ◽  
Asian Option ◽  
Underlying Asset ◽  
Average Value ◽  
Control Variate ◽  
Exercise Price ◽  
Maturity Date

Option is a contract between the writer and the holder which entitles the holder to buy or sell an underlying asset at the maturity date for a specified price known as an exercise price. Asian option is a type of financial derivatives which the payoff taking the average value over the time series of the asset price. The aim of the study is to present the Monte Carlo-Control Variate as an extension of Standard Monte Carlo applied on the calculation of the Asian option price. Standard Monte Carlo simulations 10.000.000 generate standard error 0.06 and the option price convergent at Rp.160.00 while Monte Carlo-Control Variate simulations 100.000 generate standard error 0.01 and the option price convergent at Rp.152.00. This shows the Monte Carlo-Control Variate achieve faster option price toward convergent of the Monte Carlo Standar.

scholarly journals Series representation of the pricing formula for the European option driven by space-time fractional diffusion

2018 ◽  
Vol 21 (4) ◽  
pp. 981-1004 ◽  
Author(s):  
Jean-Philippe Aguilar ◽  
Cyril Coste ◽  
Jan Korbel
Keyword(s):  
Asset Price ◽  
Series Representation ◽  
Option Price ◽  
Double Series ◽  
Fractional Diffusion ◽  
Space Time ◽  
Esscher Transform ◽  
European Option ◽  
Underlying Asset ◽  
European Call Option

Abstract In this paper, we show that the price of an European call option, whose underlying asset price is driven by the space-time fractional diffusion, can be expressed in terms of rapidly convergent double-series. This series formula is obtained from the Mellin-Barnes representation of the option price with help of residue summation in ℂ2. We also derive the series representation for the associated risk-neutral factors, obtained by Esscher transform of the space-time fractional Green functions.

scholarly journals Variance and Dimension Reduction Monte Carlo Method for Pricing European Multi-Asset Options with Stochastic Volatilities

2019 ◽  
Vol 11 (3) ◽  
pp. 815 ◽  
Author(s):  
Yijuan Liang ◽  
Xiuchuan Xu
Keyword(s):  
Monte Carlo ◽  
Variance Reduction ◽  
Convergence Rates ◽  
Option Price ◽  
Correlation Coefficients ◽  
Control Variate ◽  
Stochastic Volatilities ◽  
Conditional Monte Carlo ◽  
Mc Simulation ◽  
Martingale Representation Theorem

Pricing multi-asset options has always been one of the key problems in financial engineering because of their high dimensionality and the low convergence rates of pricing algorithms. This paper studies a method to accelerate Monte Carlo (MC) simulations for pricing multi-asset options with stochastic volatilities. First, a conditional Monte Carlo (CMC) pricing formula is constructed to reduce the dimension and variance of the MC simulation. Then, an efficient martingale control variate (CV), based on the martingale representation theorem, is designed by selecting volatility parameters in the approximated option price for further variance reduction. Numerical tests illustrated the sensitivity of the CMC method to correlation coefficients and the effectiveness and robustness of our martingale CV method. The idea in this paper is also applicable for the valuation of other derivatives with stochastic volatility.

Alternative Formulas to Compute Implied Standard Deviation

2009 ◽  
Vol 12 (02) ◽  
pp. 159-176 ◽  
Author(s):  
James S. Ang ◽  
Gwoduan David Jou ◽  
Tsong-Yue Lai
Keyword(s):  
Standard Deviation ◽  
Closed Form ◽  
Asset Price ◽  
Closed Form Solution ◽  
Form Solution ◽  
Call Option ◽  
Present Value ◽  
Underlying Asset ◽  
The Third ◽  
Exercise Price

We assume that the call option's value is correctly priced by Black and Scholes' option pricing model in this paper. This paper derives an exact closed-form solution for implied standard deviation under the condition that the underlying asset price equals the present value of the exercise price. The exact closed-form solution provides the true implied standard deviation and has no estimate error. This paper also develops three alternative formulas to estimate the implied standard deviation if this condition is violated. Application of the Taylor expansion on a single call option value derives the first formula. The accuracy of this formula depends on the deviation between the underlying asset price and the present value of the exercise price. Use of the Taylor formula on two call option prices with different exercise prices is used to develop the second formula, which can be used even though the underlying asset price deviates significantly from the present value of the exercise price. Extension of the second formula's approach to third options value derives the third formula. A merit of the third formula is to circumvent a required parameter used in the second formula. Simulations demonstrate that the implied standard deviations calculated by the second and third formulas provide accurate estimates of the true implied standard deviations.

An Empirical Study on Implied Volatility Skew Using PCA

2016 ◽  
Vol 24 (3) ◽  
pp. 365-397
Author(s):  
Jin Woo Kim ◽  
Joon H. Rhee
Keyword(s):  
Financial Crisis ◽  
Implied Volatility ◽  
Structural Changes ◽  
Explanatory Power ◽  
Asset Price ◽  
Option Price ◽  
Principal Component ◽  
Underlying Asset ◽  
Put Options ◽  
Two Factors

This paper extracts the factors determining the implied volatility skew movements of KOSPI200 index options by applying PCA (Principal Component Analysis). In particular, we analyze the movement of skew depending on the changes of the underlying asset price. As a result, it turned out that two factors can explain 94.6%~99.8% of the whole movement of implied volatility. The factor1 could be interpreted as ‘parallel shift’, and factor2 as the movement of ‘tilt or slope’. We also find some significant structural changes in the movement of skew after the Financial Crisis. The explanatory power of factor1 becomes more important on the movement of skew in both call and put options after the financial crisis. On the other hand, the influences of the factor2 is less. In general, after financial crisis, the volatility skew has the strong tendency to move in parallel. This implies that the changes in the option price or implied volatility due to the some shocks becomes more independent of the strike prices.

scholarly journals A Technical Note, Looback Options: a comparison between Monte Carlo Techniques

2020 ◽  
Vol 14 (2) ◽  
pp. 119
Author(s):  
Marcelo González A. ◽  
Antonio Parisi F. ◽  
Arturo Rodríguez P.
Keyword(s):  
Monte Carlo ◽  
Performance Measures ◽  
Asset Price ◽  
Contingent Claims ◽  
Technical Note ◽  
Time Interval ◽  
Underlying Asset ◽  
Monte Carlo Techniques ◽  
Lookback Options ◽  
Path Dependent

Looback options are path dependent contingent claims whose payoffs depend on the extrema of the underlying asset price over a certain time interval. In this note we compare the performance of two Monte Carlo techniques to price lookback options, a crude Monte Carlo estimator and Antithetic variate estimator. We find that the Antithetic estimator performs better under a variety of performance measures.

scholarly journals OPTIMAL EXERCISE PRICE OF AMERICAN OPTIONS NEAR EXPIRY

2009 ◽  
Vol 51 (2) ◽  
pp. 145-161 ◽  
Author(s):  
WEN-TING CHEN ◽  
SONG-PING ZHU
Keyword(s):  
Interest Rate ◽  
Singular Perturbation ◽  
Perturbation Methods ◽  
Asset Price ◽  
Logarithmic Factor ◽  
Underlying Asset ◽  
Singular Perturbation Methods ◽  
Exercise Price ◽  
Option Values ◽  
Numerical Approaches

AbstractThis paper investigates American puts on a dividend-paying underlying whose volatility is a function of both time and underlying asset price. The asymptotic behaviour of the critical price near expiry is deduced by means of singular perturbation methods. It turns out that if the underlying dividend is greater than the risk-free interest rate, the behaviour of the critical price is parabolic, otherwise an extra logarithmic factor appears, which is similar to the constant volatility case. The results of this paper complement numerical approaches used to calculate the option values and the optimal exercise price at times that are not close to expiry.

scholarly journals Stock Price Simulation Using Bootstrap and Monte Carlo

2017 ◽  
Vol 64 (2) ◽  
pp. 155-170 ◽  
Author(s):  
Martin Pažický
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stock Price ◽  
Error Term ◽  
Monte Carlo Experiment ◽  
Asian Option ◽  
Heteroscedastic Error ◽  
Maturity Date ◽  
The Future ◽  
The Difference

Abstract In this paper, an attempt is made to assessment and comparison of bootstrap experiment and Monte Carlo experiment for stock price simulation. Since the stock price evolution in the future is extremely important for the investors, there is the attempt to find the best method how to determine the future stock price of BNP Paribas′ bank. The aim of the paper is define the value of the European and Asian option on BNP Paribas′ stock at the maturity date. There are employed four different methods for the simulation. First method is bootstrap experiment with homoscedastic error term, second method is blocked bootstrap experiment with heteroscedastic error term, third method is Monte Carlo simulation with heteroscedastic error term and the last method is Monte Carlo simulation with homoscedastic error term. In the last method there is necessary to model the volatility using econometric GARCH model. The main purpose of the paper is to compare the mentioned methods and select the most reliable. The difference between classical European option and exotic Asian option based on the experiment results is the next aim of tis paper.

scholarly journals Valuing Derivatives in Commercial Banks of Emerging Markets - Application to Slovenian Market

Ekonomika ◽  
2005 ◽  
Vol 71 ◽  
Author(s):  
Andraž Grum
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Commercial Banks ◽  
Foreign Currency ◽  
Emerging Market ◽  
Asset Price ◽  
Underlying Asset ◽  
Pricing Options ◽  
Simulation Based ◽  
Derivative Market

In emerging market economies there is usually no institutionalised derivative market. Like in every other market-oriented economy, there exists the need for such instruments, especially in the corporate and financial sectors. In practice, the main market or position risk that a corporate sector is exposed to is the exchange rate or currency risk. The shortage of standardized derivatives is partly covered by unstandardized, tailormade derivatives issued by commercial banks to satisfy the specific needs of clients. Not surprisingly, a large portion of unstandardized derivatives issued by commercial banks comes in the type of forward agreements and I or options, with a foreign currency as the underlying asset. Because those derivatives are “tailormade”, they often have characteristics for which they can be classified as exotic derivatives. To manage efficiently the market risk, the issuer of such derivatives has to address the issue of valuation of those instruments. In practice, the most effective method of valuation of exotic derivatives has been found to be the Monte Carlo simulation based on the parametric model of the underlying asset price dynamics. Using the Monte Carlo simulation for pricing options raises several issues such as measuring the accuracy of simulated prices and determining the number of simulations required for the desired level of accuracy.

scholarly journals Pricing Vulnerable European Options under Lévy Process with Stochastic Volatility

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Chaoqun Ma ◽  
Shengjie Yue ◽  
Yishuai Ren
Keyword(s):  
Stochastic Volatility ◽  
Asset Price ◽  
Option Price ◽  
Closed Form Solution ◽  
European Option ◽  
Short Term ◽  
Underlying Asset ◽  
Asset Value ◽  
Mean Reverting Process

This paper considers the pricing issue of vulnerable European option when the dynamics of the underlying asset value and counterparty’s asset value follow two correlated exponential Lévy processes with stochastic volatility, and the stochastic volatility is divided into the long-term and short-term volatility. A mean-reverting process is introduced to describe the common long-term volatility risk in underlying asset price and counterparty’s asset value. The short-term fluctuation of stochastic volatility is governed by a mean-reverting process. Based on the proposed model, the joint moment generating function of underlying log-asset price and counterparty’s log-asset value is explicitly derived. We derive a closed-form solution for the vulnerable European option price by using the Fourier inversion formula for distribution functions. Finally, numerical simulations are provided to illustrate the effects of stochastic volatility, jump risk, and counterparty credit risk on the vulnerable option price.

COMPUTING BOUNDS ON RISK-NEUTRAL DISTRIBUTIONS FROM THE OBSERVED PRICES OF CALL OPTIONS

2010 ◽  
Vol 27 (02) ◽  
pp. 211-225
Author(s):  
MICHI NISHIHARA ◽  
MUTSUNORI YAGIURA ◽  
TOSHIHIDE IBARAKI
Keyword(s):  
Lower Bounds ◽  
Asset Price ◽  
Option Price ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Upper And Lower Bounds ◽  
Underlying Asset ◽  
No Arbitrage ◽  
Call Options ◽  
Risk Neutral

This paper derives, in closed forms, upper and lower bounds on risk-neutral cumulative distribution functions of the underlying asset price from the observed prices of European call options, based only on the no-arbitrage assumption. The computed bounds from the option price data show that the gap between the upper and lower bounds is large near the underlying asset price but gets smaller away from the underlying asset price. Since the bounds can be easily computed and visualized, they could be practically used by investors in various ways.

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