StudentShare solutions

# Pricing of derivatives on mean-reverting assets. Are stock prices and returns are mean reverting or not - Essay Example

## Extract of samplePricing of derivatives on mean-reverting assets. Are stock prices and returns are mean reverting or not

15 3.6 Data Analysis Methods ……………………………………………………. 16 3.7 Summary …………………………………………………………………… 16 CHAPTER 4 ………………………………………………………………………….……. 17 FIGURES ………………………………...………………………………………… 17 4.1 Definition of mean reversion stock prices ……………………………….…….. 17 4.2 Permanent and transitory price components …………………………………… 17 4.3 Properties of multi-period returns ……………………………………….……... 18 4.4 One-period returns ……………………………………………………....…..…. 19 4.5 Multi-period returns ……………………………………………………………. 20 4.6 Higher-order AR model ……………………………………………………….... 22 4.7 The relation between mean reversion and covariance stationary …...………….. 23 CHAPTER 5 …………………………………………………………………………………… 25 5. Mean reversion and mean-variance efficient portfolios …………………………. 25 5.1 Outline ………………………………………………………………………….. 25 5.1.1 Expected returns and volatilities of stocks and bonds ………………... 25 5.1.2 Correlation between stock and bond returns …………………………. 26 5.1.3 Risk-free yield curve …………………………………………………. 26 5.1.4 Variance ratio of permanent and transitory returns …………….…….. 26 5.2 The role of the variance ratio...
Although the mean-reverting price process defined later by Equations (1), (2), and (3) may seem restrictive, they are more general than is apparent at first sight. This generality explains the model’s suitability as a tool for describing the mean reverting behavior of stock prices. To allow the price process to be consistent with the efficient market hypothesis, the random walk should lie nested in the specification for the stock price (Frankel, 1995, 140). This explains why the permanent price component in the first equation lies chosen to be a random walk. The price process in Equation (1) follows a random walk for ø= one, but deviates from the efficient market hypothesis for zero < ø < 1. Hence, only the choice for a first-order autoregressive (AR) process could possibly be restrictive (Bekaert, 1999, 129).

A seemingly more general specification defines zt with regard to the first equation as a covariance-stationary, mean-reverting process with mean 0.But every covariance stationary series can stand written as a moving average (MA) process of infinite order. If the MA process is invertible, it can be written as an AR process of infinite order, which brings us one-step closer to our AR (1) process. The only restrictive aspect of the first-order AR process is its order. We may therefore want to consider a generalization of the previously considered mean reverting price process by relaxing the assumption of a first order AR process for the transitory price component. Instead of an AR (1) process we could assume an AR (p) process as approximation of an AR process of infinite order, for any p= one, 2… (Bekaert, 1999, 65). ...Show more

## Summary

The goal of this paper is not to provide a final answer to the question whether stock prices and returns are mean reverting or not. Instead, the research aims at making investors aware of the economic consequences of mean reverting behavior of stocks. This lies in regard with the Mondale as of 2022. …
Author : xtorp
Save Your Time for More Important Things
Let us write or edit the essay on your topic
"Pricing of derivatives on mean-reverting assets. Are stock prices and returns are mean reverting or not"
with a personal 20% discount.
Grab the best paper

### Check these samples - they also fit your topic

Mean-Variance Analysis
A method such as mean-variance analysis helps predict and reduce the amount of risk in an investment. Holding a mix of assets, otherwise known as portfolio diversification, is a key concept upon which successful investments in the business world gain greater practicability and predictability.
6 pages (1500 words) Essay
Mean girls movie analysis
This film shows the social hegemony, which female teens are exposed to while studying in high school. Here the supreme social group simply remains in control just because the rest allow them to. By knowing their position, they generate fear, which enables them to keep the position and helps evade being overthrown (Cragan and Wright 123).
4 pages (1000 words) Essay
Mean World Syndrome
As a result, the opinions, graphics and attitudes that an individual will see or hear through any mass media channel will influence their personal opinions as well as their attitude towards the environment that they are in. Gerbner once mentioned that, "You know, who tells the stories of a culture really governs human behaviour.
5 pages (1250 words) Essay
Explain why rising prices do not necesssarily mean declining living standards
But it was not possible to measure he amount of happiness so they changed its meaning and attach it with real income. Real income is money which is adjusted for the cost of living, also for the achieving things such as health, education and
4 pages (1000 words) Essay
Mean girls movie analysis
Here the supreme social group simply remains in control simply because the rest allow them to. By knowing their position, they generate fear, thus enabling them to keep their position hence evading being overthrown (John F., David W 123). In the
4 pages (1000 words) Essay
Assets pricing
The main advantages of using this methodology include assistance in doing accurate statistical analysis and assistance in complex financial calculations. The performance of
4 pages (1000 words) Essay
Mean Girls
society and the globe at large has seen many people, especially the youths, suppressed and put off from exploiting their maximum potential in various avenues of life, including education and careers (Vena and Kash, 2009). The black community has been on the receiving end of
3 pages (750 words) Essay
Disability Does Not Mean Inability
Sport, business, politics, education, healthcare have become the most striking platforms where these achievements are evident. Of
3 pages (750 words) Essay
Modern pricing models
As such, he named the financial model after himself, the Heston Model. As such, he was able to develop a model that provided pricing options with a closed-form solution in an attempt to overcome
1 pages (250 words) Essay
Modern pricing models
the paper also discusses the Merton model of jump diffusion as a financial analysis model, and its application in finance, its uses and properties, alongside its relationship to the Black-Scholes model. the other pricing model explored in this paper is the Fisher Black
10 pages (2500 words) Essay
Get a custom paper written
by a pro under your requirements!
Win a special DISCOUNT!
Put in your e-mail and click the button with your lucky finger