Stochastic differential equations and diffusion processes

The paper is based on the observations that stockk index returns of major equity markets are likely to be Student t distributed. It then develops a class of continuous time stochastic volatility models that is consistent with such empirical findings. Furthermore, applying the criterion of local risk minimisation in an incomplete market setting, option prices are computed. Finally it is shown that implied volatility smile and skew patterns of the type observed in the markets can be recovered from the resulting stochastic volatility model.

Modelling the Stochastic Dynamics of Volatility for Equity Indices

We construct two classes of risk-reward measures - one by generalizing the mean-variance model of Markowitz (1952), and the other by generalizing the gain-loss model of Bernardo & Ledoit (2000) - and develop, for these economies, the following: (i) a CAPM-like relative pricing equation; (ii) an analytical expression for the associated stochastic discount factor (pricing kernel) as a (generally) nonlinear function of the market excess return; (iii) explicit analytical solutions in the complete markets case for optimal portfolios, and the maximum possible reward-to-risk ratio (akin to the Sharpe ratio), as functions of the economy's complete markets discount factor; (iv) an equivalent non-Expected Utility Theory (non-EUT) value function, and (v) a simplified market factor model along the lines of Sharpe (1963). Multifactor extensions, and econometric considerations, are also taken up. It is argued that the generalized Markowitz model has the potential to outperform the Sharpe-Lintner CAPM, and to capture segmentation in asset markets via its variable risk proxy. The generalized Bernardo-Ledoit model's non-EUT value function is shown, in the appropriate parameter regime, to reduce to the S-shaped value function of a loss-averse investor (Prospect Theory, Kahneman and Tversky, 1979). It is further shown that a loss-averse representative agent's optimal zero-cost portfolio payoff (excess return) in a complete markets setting is strictly positive in all future states of nature except one, where it is strictly negative. The asymmetry in positive and negative state-specific payoffs is found to decrease as the market becomes more incomplete. Our CAPM-like models are in a sufficient state of development to be tested directly against market data.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID931552_code634178.pdf?abstractid=931552&mirid=1&type=2

Risk, Reward and Asset Pricing

We establish simple analytical and numerical methods for propagating stochastic price processes backwards in time, step by step, to the initial value while satisfying a ll cross-sectional and serial requirements. This proves useful in dealing with complex path-dependent options with American triggers, where storing the history of the underlying can become computationally onerous. Examples involving the Wiener, Ornstein-Uhlenbeck, Clark, and Cox-IngersollRoss processes illustrate our techniques. In particular, w e examine the use of the “just-in-time” method for the pricing of mortgages with embedded prepayment and default options.

Just-In-Time Monte Carlo for MBS Valuation

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Samir K. Dutt

Author Tools

Chat about Author

Papers

Risk, Reward and Asset Pricing

Just-In-Time Monte Carlo for MBS Valuation