Modigliani Miller Investment Implications: A Put Option Theory of Capital Structure and Stochastic Volatility

2011 ◽  
Author(s):  
William A. Barr
Keyword(s):  
Capital Structure ◽  
Stochastic Volatility ◽  
Put Option ◽  
Option Theory

scholarly journals Pricing of American Put Option under a Jump Diffusion Process with Stochastic Volatility in an Incomplete Market

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Shuang Li ◽  
Yanli Zhou ◽  
Xinfeng Ruan ◽  
B. Wiwatanapataphee
Keyword(s):  
Diffusion Process ◽  
Stochastic Volatility ◽  
American Options ◽  
Option Price ◽  
Jump Diffusion ◽  
Incomplete Market ◽  
American Put Option ◽  
Put Option ◽  
Jump Diffusion Process ◽  
American Put

We study the pricing of American options in an incomplete market in which the dynamics of the underlying risky asset is driven by a jump diffusion process with stochastic volatility. By employing a risk-minimization criterion, we obtain the Radon-Nikodym derivative for the minimal martingale measure and consequently a linear complementarity problem (LCP) for American option price. An iterative method is then established to solve the LCP problem for American put option price. Our numerical results show that the model and numerical scheme are robust in capturing the feature of incomplete finance market, particularly the influence of market volatility on the price of American options.

The stochastic-volatility American put option of banks' credit line commitments:

2002 ◽  
Vol 11 (2) ◽  
pp. 159-181 ◽  
Author(s):  
J.-P. Chateau ◽  
D. Dufresne
Keyword(s):  
Stochastic Volatility ◽  
American Put Option ◽  
Credit Line ◽  
Put Option ◽  
American Put

scholarly journals Stochastic Volatility Estimation of Stock Prices using the Ensemble Kalman Filter

2021 ◽  
Vol 3 (2) ◽  
pp. 136-143
Author(s):  
Yudi Mahatma ◽  
Ibnu Hadi
Keyword(s):  
Kalman Filter ◽  
Interest Rate ◽  
Interest Rates ◽  
State Space ◽  
Stochastic Volatility ◽  
Ensemble Kalman Filter ◽  
Price Volatility ◽  
Call Option ◽  
Put Option ◽  
Black Scholes

AbstractVolatility plays important role in options trading.  In their seminal paper published in 1973, Black and Scholes assume that the stock price volatility, which is the underlying security volatility of a call option, is constant.  But thereafter, researchers found that the return volatility was not constant but conditional to the information set available at the computation time.  In this research, we improve a methodology to estimate volatility and interest rate using Ensemble Kalman Filter (EnKF).  The price of call and put option used in the observation and the forecasting step of the EnKF algorithm computed using the solution of Black-Scholes PDE.  The state-space used in this method is the augmented state space, which consists of static variables: volatility and interest rate, and dynamic variables: call and put option price. The numerical experiment shows that the EnKF algorithm is able to estimate accurately the estimated volatility and interest rates with an RMSE value of 0.0506.Keywords: stochastic volatility; call option; put option; Ensemble Kalman Filter. AbstrakVolatilitas adalah faktor penting dalam perdagangan suatu opsi.  Dalam makalahnya yang dipublikasikan tahun 1973, Black dan Scholes mengasumsikan bahwa volatilitas harga saham, yang merupakan volatilitas sekuritas yang mendasari opsi beli, adalah konstan. Akan tetapi, para peneliti menemukan bahwa volatilitas pengembalian tidaklah konstan melainkan tergantung pada kumpulan informasi yang dapat digunakan pada saat perhitungan.  Pada penelitian ini dikembangkan metodologi untuk mengestimasi volatilitas dan suku bunga menggunakan metode Ensembel Kalman Filter (EnKF).  Harga opsi beli dan opsi jual yang digunakan pada observasi dan pada tahap prakiraan pada algoritma EnKF dihitung menggunakan solusi persamaan Black-Scholes.  Ruang keadaan yang digunakan adalah ruang keadaan yang diperluas yang terdiri dari variabel statis yaitu volatilitas dan suku bunga, dan variabel dinamis yaitu harga opsi beli dan harga opsi jual. Eksperimen numerik menunjukkan bahwa algoritma ENKF dapat secara akurat mengestimasi volatiltas dan suku bunga dengan RMSE 0.0506.Kata kunci: volatilitas stokastik; opsi beli; opsi jual; Ensembel Kalman Filter.

Pricing multi-asset American option under Heston stochastic volatility model

2018 ◽  
Vol 05 (03) ◽  
pp. 1850026 ◽  
Author(s):  
Oldouz Samimi ◽  
Farshid Mehrdoust
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Discretization Scheme ◽  
Put Option ◽  
Volatility Model ◽  
Discretization Schemes ◽  
Multiple Assets ◽  
American Put

In this paper, we employ the Least-Squares Monte-Carlo (LSM) algorithm regarding three discretization schemes, namely, the Euler–Maruyama discretization scheme, the Milstein scheme and the Quadratic Exponential (QE) scheme to price the multiple assets American put option under the Heston stochastic volatility model. Some numerical results are presented to demonstrate the effectiveness of the proposed methods.

SHOULD AN AMERICAN OPTION BE EXERCISED EARLIER OR LATER IF VOLATILITY IS NOT ASSUMED TO BE A CONSTANT?

2011 ◽  
Vol 14 (08) ◽  
pp. 1279-1297 ◽  
Author(s):  
SONG-PING ZHU ◽  
WEN-TING CHEN
Keyword(s):  
Stochastic Volatility ◽  
Option Price ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Put Options ◽  
American Put Option ◽  
Put Option ◽  
Exercise Price ◽  
Volatility Model ◽  
American Put

In this paper, we present a correction to Merton (1973)'s well-known classical case of pricing perpetual American put options by considering the same pricing problem under a stochastic volatility model with the assumption that the volatility is slowly varying. Two analytic formulae for the option price and the optimal exercise price of a perpetual American put option are derived, respectively. Upon comparing the results obtained from our analytic approximations with those calculated by a spectral collocation method, it is shown that our current approximation formulae provide fast and reasonably accurate numerical values of both option price and the optimal exercise price of a perpetual American put option, within the validity of the assumption we have made for the asymptotic expansion. We shall also show that the range of applicability of our formulae is remarkably wider than it was initially aimed for, after the original assumption on the order of the "volatility of volatility" being somewhat relaxed. Based on the newly-derived formulae, the quantitative effect of the stochastic volatility on the optimal exercise strategy of a perpetual American put option has also been discussed. A most noticeable and interesting result is that there is a special cut-off value for the spot variance, below which a perpetual American put option priced under the Heston model should be held longer than the case of the same option priced under the traditional Black-Scholes model, when the price of the underlying is falling.

scholarly journals The Correction of Multiscale Stochastic Volatility to American Put Option: An Asymptotic Approximation and Finite Difference Approach

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Yanli Zhou ◽  
Shican Liu ◽  
Shuang Li ◽  
Xiangyu Ge
Keyword(s):  
Finite Difference ◽  
Stochastic Volatility ◽  
Asymptotic Approximation ◽  
Implied Volatility ◽  
Option Price ◽  
Stochastic Volatility Model ◽  
American Put Option ◽  
Put Option ◽  
Volatility Model ◽  
American Put

It has been found that the surface of implied volatility has appeared in financial market embrace volatility “Smile” and volatility “Smirk” through the long-term observation. Compared to the conventional Black-Scholes option pricing models, it has been proved to provide more accurate results by stochastic volatility model in terms of the implied volatility, while the classic stochastic volatility model fails to capture the term structure phenomenon of volatility “Smirk.” More attempts have been made to correct for American put option price with incorporating a fast-scale stochastic volatility and a slow-scale stochastic volatility in this paper. Given that the combination in the process of multiscale volatility may lead to a high-dimensional differential equation, an asymptotic approximation method is employed to reduce the dimension in this paper. The numerical results of finite difference show that the multiscale volatility model can offer accurate explanations of the behavior of American put option price.

Sign in / Sign up

Export Citation Format

Share Document