Pathwise estimation and inference for diffusion market models

Pathwise estimation and inference for diffusion market models /

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Bibliographic Details
Main Authors: Dokuchaev, Nikolai (Author), Hin, Lin Yee (Author)
Corporate Author: ProQuest (Firm)
Format: Electronic eBook
Language:English
Published: Boca Raton : CRC, Taylor & Francis Group, 2019.
Subjects:
Estimation theory.
Capital market > Mathematical models.
Online Access:Connect to this title online (unlimited simultaneous users allowed; 325 uses per year)

MARC

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100 1 |a Dokuchaev, Nikolai,  |e author. 
245 1 0 |a Pathwise estimation and inference for diffusion market models /  |c Nikolai Dokuchaev, Lin Yee Hin. 
264 1 |a Boca Raton :  |b CRC, Taylor & Francis Group,  |c 2019. 
300 |a 1 online resource (224 pages) :  |b illustrations. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
505 0 0 |a Machine generated contents note:   |g 1.  |t Some background on stochastic analysis --   |g 1.1.  |t Basics of probability theory --   |g 1.1.1.  |t Probability space --   |g 1.1.2.  |t Random variables --   |g 1.1.3.  |t Expectations --   |g 1.1.4.  |t Conditional probability and expectation --   |g 1.1.5.  |t σ-algebra generated by a random vector --   |g 1.2.  |t Basics of stochastic processes --   |g 1.2.1.  |t Special classes of processes --   |g 1.2.2.  |t Wiener process (Brownian motion) --   |g 1.3.  |t Basics of the stochastic calculus (Ito calculus) --   |g 1.3.1.  |t Ito formula --   |g 1.3.2.  |t Stochastic differential equations (Ito equations) --   |g 1.3.3.  |t Some explicit solutions for Ito equations --   |g 1.3.4.  |t Diffusion Markov processes and related parabolic equations --   |g 1.3.5.  |t Martingale representation theorem --   |g 1.3.6.  |t Change of measure and Girsanov theorem --   |g 2.  |t Some background on diffusion market models --   |g 2.1.  |t Continuous time model for stock price --   |g 2.2.  |t Continuous time bond-stock market model --   |g 2.3.  |t Discounted wealth and stock prices --   |g 2.4.  |t Risk-neutral measure --   |g 2.5.  |t Replicating strategies --   |g 2.6.  |t Arbitrage possibilities and the arbitrage-free market --   |g 2.7.  |t case of a complete market --   |g 2.8.  |t Completeness of the Black-Scholes model --   |g 2.9.  |t Option pricing --   |g 2.9.1.  |t Options and their prices --   |g 2.9.2.  |t Option pricing for a complete market --   |g 2.9.3.  |t Black-Scholes formula --   |g 2.10.  |t Pricing for an incomplete market --   |g 2.11.  |t multi-stock market model --   |g 3.  |t Some special market models --   |g 3.1.  |t Mean-reverting market model --   |g 3.1.1.  |t Basic properties of a mean-reverting model --   |g 3.1.2.  |t Absence of arbitrage and the Novikov condition --   |g 3.1.3.  |t Proofs --   |g 3.2.  |t market model with delay in coefficients --   |g 3.2.1.  |t Existence, regularity, and non-arbitrage properties --   |g 3.2.2.  |t Time discretization and restrictions on growth --   |g 3.3.  |t market model with stochastic numeraire --   |g 3.3.1.  |t Model setting --   |g 3.3.2.  |t Replication of claims: Strategies and hedging errors --   |g 3.3.3.  |t On selection of θ and the equivalent martingale measure --   |g 3.3.4.  |t Markov case --   |g 3.3.5.  |t Proofs --   |g 3.4.  |t Bibliographic notes and literature review --   |g 4.  |t Path wise inference for the parameters of market models --   |g 4.1.  |t Estimation of volatility --   |g 4.1.1.  |t Representation theorems for the volatility --   |g 4.1.2.  |t Estimation of discrete time samples --   |g 4.1.3.  |t Reducing the impact of the appreciation rate --   |g 4.1.4.  |t algorithm --   |g 4.1.5.  |t Some experiments --   |g 4.2.  |t Modeling the impact of the sampling frequency --   |g 4.2.1.  |t Analysis of the model's parameters --   |g 4.2.2.  |t Monte Carlo simulation of the process with delay --   |g 4.2.3.  |t Examples for dependence of volatility on sampling frequency for historical data --   |g 4.2.4.  |t Matching delay parameters for historical data --   |g 4.3.  |t Inference for diffusion parameters for CIR-type models --   |g 4.3.1.  |t underlying continuous time model --   |g 4.3.2.  |t representation theorem for the diffusion coefficient --   |g 4.3.3.  |t Estimation based on the representation theorem --   |g 4.3.4.  |t Numerical experiments --   |g 4.3.5.  |t On the consistency of the method --   |g 4.3.6.  |t Some properties of the estimates --   |g 4.4.  |t Estimation of the appreciation rates --   |g 4.5.  |t Bibliographic notes and literature review --   |g 5.  |t Some background on bond pricing --   |g 5.1.  |t Zero-coupon bonds --   |g 5.2.  |t One-factor model --   |g 5.2.1.  |t Dynamics of discounted bond prices --   |g 5.2.2.  |t Dynamics of the bond prices under the original measure --   |g 5.2.3.  |t example: The Cox-Ross-Ingresoll model --   |g 5.3.  |t Vasicek model --   |g 5.4.  |t example of a multi-bond market model --   |g 6.  |t Implied volatility and other implied market parameters --   |g 6.1.  |t Risk-neutral pricing in a Black--Scoles setting --   |g 6.2.  |t Implied volatility: The case of constant τ --   |g 6.3.  |t Correction of the volatility smile for constant τ --   |g 6.3.1.  |t Imperfection of the volatility smile for constant τ --   |g 6.3.2.  |t pricing rule correcting the volatility smile --   |g 6.3.3.  |t class of volatilities in a Markovian setting --   |g 6.4.  |t Unconditionally implied volatility and risk-free rate --   |g 6.4.1.  |t Two calls with different strike prices --   |g 6.5.  |t Bond price inferred from option prices --   |g 6.5.1.  |t Definitions --   |g 6.5.2.  |t Inferred p from put and call prices --   |g 6.5.3.  |t Application to a special model --   |g 6.6.  |t dynamically purified option price process --   |g 6.7.  |t implied market price of risk with random numeraire --   |g 6.7.1.  |t risk-free bonds for the market with random numeraire --   |g 6.7.2.  |t case of a complete market --   |g 6.7.3.  |t case of an incomplete market --   |g 6.8.  |t Bibliographic notes --   |g 7.  |t Inference of implied parameters from option prices --   |g 7.1.  |t Sensitivity analysis of implied volatility estimation --   |g 7.1.1.  |t under-defined system of nonlinear equations --   |g 7.1.2.  |t Numerical analysis using cross-sectional S&P 500 call options data --   |g 7.1.3.  |t Numerical analysis using longitudinal S&P500 call options data --   |g 7.2.  |t brief review of evolutionary optimization --   |g 7.2.1.  |t original differential evolution algorithm --   |g 7.2.2.  |t Zhang-Sanderson adaptive differential evolution algorithms --   |g 7.3.  |t Inference of implied parameters from over-defined systems --   |g 7.3.1.  |t over-defined system of nonlinear equations --   |g 7.3.2.  |t Computational implementation --   |g 7.3.3.  |t Construction of the estimation uncertainty bounds for the estimated implied discount rates and implied volatilities --   |g 7.3.4.  |t Numerical experiment with synthetic test data --   |g 7.3.5.  |t Numerical analysis using historical S&P500 call options data --   |g 7.4.  |t Bibliographic notes and literature review --   |g 8.  |t Forecast of short rate based on the CIR model --   |g 8.1.  |t model framework --   |g 8.1.1.  |t General setting --   |g 8.1.2.  |t CIR model --   |g 8.2.  |t Inference of the implied CIR model parameters based on cross-sectional zero coupon bond prices --   |g 8.3.  |t Numerical framework for the inference --   |g 8.4.  |t Computational implementation --   |g 8.5.  |t Forecast of short rate using the implied CIR model parameters --   |g 8.5.1.  |t Forecast within the multi-curve framework --   |g 8.5.2.  |t Forecast within the single-curve framework --   |g 8.6.  |t Numerical analysis using historical data --   |g 8.6.1.  |t Short rate prediction in the multi-curve framework --   |g 8.6.2.  |t Short rate prediction in the single-curve framework --   |g 8.7.  |t Bibliographic notes and literature review. 
533 |a Electronic reproduction.  |b Ann Arbor, MI  |n Available via World Wide Web. 
588 |a Description based on print version record. 
650 0 |a Estimation theory. 
650 0 |a Capital market  |x Mathematical models. 
700 1 |a Hin, Lin Yee,  |e author. 
710 2 |a ProQuest (Firm) 
776 0 8 |i ebook version :  |z 9780429948855 
776 0 8 |c Original  |z 1138591645  |z 9781138591646 
856 4 0 |u https://ebookcentral.proquest.com/lib/santaclara/detail.action?docID=5741574  |z Connect to this title online (unlimited simultaneous users allowed; 325 uses per year)  |t 0 
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