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.

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.

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.

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