Showing papers on "Binomial options pricing model published in 2021"
24 Jun 2021
TL;DR: In this paper, a quantum algorithm for stochastic differential equations (SDEs) is proposed, which gives a quadratic speedup for multilevel Monte Carlo methods in a general setting.
Abstract: Inspired by recent progress in quantum algorithms for ordinary and partial differential equations, we study quantum algorithms for stochastic differential equations (SDEs). Firstly we provide a quantum algorithm that gives a quadratic speed-up for multilevel Monte Carlo methods in a general setting. As applications, we apply it to compute expectation values determined by classical solutions of SDEs, with improved dependence on precision. We demonstrate the use of this algorithm in a variety of applications arising in mathematical finance, such as the Black-Scholes and Local Volatility models, and Greeks. We also provide a quantum algorithm based on sublinear binomial sampling for the binomial option pricing model with the same improvement.
14 citations
Book•
09 Jul 2021
TL;DR: In this article, the authors present a model for risk-neutral pricing in the (B, S) economy with a single-period Arrow-Debreu model and a continuous-time Stochastic calculus.
Abstract: INTRODUCTION TO PRICING AND MANAGEMENT OF FINANCIAL SECURITIES Mathematics of Compounding Primer on Pricing Risky Securities Portfolio Management Primer on Derivative Securities DISCRETE-TIME MODELING Single-Period Arrow-Debreu Models Introduction to Discrete-Time Stochastic Calculus Replication and Pricing in the Binomial Tree Model General Multi-Asset Multi-Period Model CONTINUOUS-TIME MODELING Essentials of General Probability Theory One-Dimensional Brownian Motion and Related Processes Introduction to Continuous-Time Stochastic Calculus Risk-Neutral Pricing in the (B, S) Economy: One Underlying Stock Risk-Neutral Pricing in a Multi-Asset Economy American Options Alternative Models of Asset Price Dynamics Interest-Rate Modeling and Derivative Pricing COMPUTATIONAL TECHNIQUES Introduction to Monte Carlo and Simulation Methods Numerical Applications to Derivative Pricing Appendix: Some Useful Integral Identities and Symmetry Properties of Normal Random Variables Glossary of Symbols and Abbreviations References Index
13 citations
TL;DR: Wang et al. as mentioned in this paper applied real option theory to evaluate the uncertainty of a Shared WSMC project and the economic feasibility of investing in the project, and the obtained results indicate that the economic value of the Shared WMC project is expanded by the ROV, which means that additional value can be gained through flexible strategies and management.
13 citations
TL;DR: In this article, the American option pricing procedure based on the binomial tree from an imprecise statistical aspect is presented, and nonparametric predictive inference (NPI) is implemented to infer the price of an option.
Abstract: In this article, we present the American option pricing procedure based on the binomial tree from an imprecise statistical aspect. Nonparametric Predictive Inference (NPI) is implemented to infer i...
5 citations
TL;DR: In this article, the Sari Gunay gold mine's production planning was evaluated by Taylor and Zwiagin methods with 22 different scenarios in all conditions, including (a) price certainty and uncertainty such as daily price, 3-and 5-year average, Monte Carlo simulation, and binomial tree; (b) decreasing, increasing, and fixed production rates; and (c) mine life conditions.
Abstract: Due to the long life, most mining projects face the risk of the parameters such as mineral price, grade, and cost. Uncertainty can lead to unfavorable results of the decisions made by managers and mining investors. Therefore, this paper aims to determine the Sari Gunay gold mine’s production planning, considering the certainty and uncertainty over the mineral price. Finally, the proposed planning will lead to the allocation of fixed or variable production rates throughout the mine life. These findings were assessed by Taylor and Zwiagin methods with 22 different scenarios in all conditions, including (a) price certainty and uncertainty such as daily price, 3- and 5-year average, Monte Carlo simulation, and binomial tree; (b) decreasing, increasing, and fixed production rates; and (c) mine life conditions. The scenarios evaluated under the price certainty conditions (scenarios 1 to 12) have lower NPV values than those under the price uncertainty conditions. This is because the price is fixed throughout the mine life. Due to historical price data and high fluctuations of estimated prices, this method’s NPV values fluctuate more than other scenarios evaluated by the Monte Carlo simulation. The binomial tree method scenarios have the lowest NPV value’s fluctuation because the fluctuation of the estimated prices is controlled, and the highest NPV values are related to this method. Out of the 22 scenarios, scenario 17 has the highest NPV value ($512,642,774). According to this scenario, the mine plan is determined, and the annual production rate is reduced to 3,241,977 tons in the first year and 270,165 tons in the last year with the Taylor life of 12 years.
5 citations
TL;DR: In this article, the authors explore option-implied information measures for optimal portfolio allocation, using a combination of statistical and economic measures applied to a portfolio given by the 1-month US Treasury bill and the S&P 500 Index.
Abstract: This paper explores option‐implied information measures for optimal portfolio allocation. We introduce two state variables constructed from option prices. The first state variable is the risk‐premium on the risky asset and the second variable is the market price of risk. We also explore a lognormal distribution, a mixture of lognormal distributions, and a binomial tree for constructing the implied risk‐neutral density function. Using a combination of statistical and economic measures applied to a portfolio given by the 1‐month US Treasury bill and the S&P 500 Index we show the good performance of option‐implied information measures for optimal portfolio allocation.
3 citations
TL;DR: In this paper, a fuzzy real options binomial tree pricing model is developed to assess the project value of ship investments based on the calculations and analysis of an actual ship investment case, fitting more closely the actual market and operating situation.
Abstract: The global shipping market has been depressed and turbulent since 2008. Shipping companies have had to be more cautious with their investments, so as to buck the trend and get through this difficult period. Traditional net present value methods cannot help enterprises make effective investment decisions. Therefore, we employ real options theory—including expansion options, contraction options, deferral options, and abandonment options—to simulate various types of operational adjustment strategies used by investors in the process of ship investment and operations. Triangular fuzzy numbers and the generalized autoregressive conditional heteroscedasticity model are also introduced to describe the uncertainty and volatility of the shipping market. Subsequently, a fuzzy real options binomial tree pricing model is developed to assess the project value of ship investments. Based on the calculations and analysis of an actual ship investment case, the fuzzy real options method is shown to be more suitable for ship investment analysis, fitting more closely the actual market and operating situation.
2 citations
TL;DR: In this paper, the authors put an uncertainty factor into volatility, assume investors minimize the root mean square error of replication when they choose hedging ratio, and derive European option price by a recursive procedure.
Abstract: To price options using replication in imperfect markets, both Knightian uncertainty and transaction cost have to be taken into account. In this paper, we put an uncertainty factor into volatility, assume investors minimize the root mean square error of replication when they choose hedging ratio, and derive European option price by a recursive procedure. To avoid high transaction cost caused by continuous hedging, we establish a discrete and binomial replication model considering both uncertainty and transaction cost. Numerical examples imply that option price contains both risk premium and uncertainty premium, and it is an approximately linearly increasing function of transaction cost but a nonlinearly increasing function of uncertainty. Additionally, both uncertainty and transaction cost have effects on the price of the at-the-money option, but they almost have no impact on the price of deeply in-the-money or out-of-the-money options. Empirical analysis of the Shanghai 50ETF options market indicates that the Black–Scholes model tended to underestimate the market price, whereas our model better estimates market prices.
1 citations
Posted Content•
TL;DR: In this article, a generalized Jarrow-Rudd (GJR) option pricing model with uncertainty driven by a skew random walk is introduced, based on the Cherny-Shiryaev-Yor invariance principle.
Abstract: Applying the Cherny-Shiryaev-Yor invariance principle, we introduce a generalized Jarrow-Rudd (GJR) option pricing model with uncertainty driven by a skew random walk. The GJR pricing tree exhibits skewness and kurtosis in both the natural and risk-neutral world. We construct implied surfaces for the parameters determining the GJR tree. Motivated by Merton's pricing tree incorporating transaction costs, we extend the GJR pricing model to include a hedging cost. We demonstrate ways to fit the GJR pricing model to a market driver that influences the price dynamics of the underlying asset. We supplement our findings with numerical examples.
Posted Content•
TL;DR: In this paper, an extension of the Cox-Ross-Rubinstein (CRR) model based on q-binomial random walks is proposed, with application to default with logistic failure rates.
Abstract: We propose an extension of the Cox-Ross-Rubinstein (CRR) model based on q-binomial (or Kemp) random walks, with application to default with logistic failure rates. This model allows us to consider time-dependent switching probabilities varying according to a trend parameter, and it includes tilt and stretch parameters that control increment sizes. Option pricing formulas are written using q-binomial coefficients, and we study the convergence of this model to a Black-Scholes type formula in continuous time. A convergence rate of order O(1/N) is obtained when the tilt and stretch parameters are set equal to one.
Dissertation•
01 Jan 2021