The Impact of Deviations from Random Walk in Security Prices on Option Prices

1998 ◽  
Author(s):  
Thomas Henker ◽  
Hossein B. Kazemi
Keyword(s):  
Random Walk ◽  
Option Prices ◽  
Security Prices ◽  
The Impact

scholarly journals Randomized Binomial Tree and Pricing of American-Style Options

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hu Xiaoping ◽  
Cao Jie
Keyword(s):  
American Option ◽  
Option Prices ◽  
Occurrence Probability ◽  
Binomial Tree ◽  
No Arbitrage ◽  
Complete Market ◽  
Cubic Polynomial ◽  
American Style ◽  
The Impact ◽  
And Storage

Randomized binomial tree and methods for pricing American options were studied. Firstly, both the completeness and the no-arbitrage conditions in the randomized binomial tree market were proved. Secondly, the description of the node was given, and the cubic polynomial relationship between the number of nodes and the time steps was also obtained. Then, the characteristics of paths and storage structure of the randomized binomial tree were depicted. Then, the procedure and method for pricing American-style options were given in a random binomial tree market. Finally, a numerical example pricing the American option was illustrated, and the sensitivity analysis of parameter was carried out. The results show that the impact of the occurrence probability of the random binomial tree environment on American option prices is very significant. With the traditional complete market characteristics of random binary and a stronger ability to describe, at the same time, maintaining a computational feasibility, randomized binomial tree is a kind of promising method for pricing financial derivatives.

Option pricing under the fractional stochastic volatility model

2021 ◽  
Vol 63 ◽  
pp. 123-142
Author(s):  
Yuecai Han ◽  
Zheng Li ◽  
Chunyang Liu
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Fractional Brownian Motion ◽  
Stochastic Volatility ◽  
Option Price ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
European Call Option ◽  
Volatility Model ◽  
The Impact

We investigate the European call option pricing problem under the fractional stochastic volatility model. The stochastic volatility model is driven by both fractional Brownian motion and standard Brownian motion. We obtain an analytical solution of the European option price via the Itô’s formula for fractional Brownian motion, Malliavin calculus, derivative replication and the fundamental solution method. Some numerical simulations are given to illustrate the impact of parameters on option prices, and the results of comparison with other models are presented. doi:10.1017/S1446181121000225

Temporal aggregation of random walk processes and implications for economic analysis

2019 ◽  
Vol 24 (2) ◽  
Author(s):  
Yamin S Ahmad ◽  
Ivan Paya
Keyword(s):  
Random Walk ◽  
Autoregressive Process ◽  
Potential Effect ◽  
Temporal Aggregation ◽  
Time Averaging ◽  
Fat Tails ◽  
Data Generating Process ◽  
Variance Ratios ◽  
Interval Sampling ◽  
The Impact

AbstractThis paper examines the impact of time averaging and interval sampling data assuming that the data generating process for a given series follows a random walk with iid errors. We provide exact expressions for the corresponding variances, and covariances, for both levels and higher order differences of the aggregated series, as well as that for the variance ratio, demonstrating exactly how the degree of temporal aggregation impacts these properties. We empirically investigate this issue on exchange rates and find that the values of the variance ratios and autocorrelation coefficients at different frequencies are consistent with our theoretical results. We also conduct a simulation exercise that illustrates the potential effect that conditional heteroskedasticity and fat tails may have on the temporal aggregation of a random walk and of a highly persistent autoregressive process.

scholarly journals ANALYSIS OF MARKET VOLATILITY VIA A DYNAMICALLY PURIFIED OPTION PRICE PROCESS

2014 ◽  
Vol 09 (03) ◽  
pp. 1450006 ◽  
Author(s):  
CHUONG LUONG ◽  
NIKOLAI DOKUCHAEV
Keyword(s):  
Stock Price ◽  
Implied Volatility ◽  
Financial Time Series ◽  
Option Price ◽  
Option Prices ◽  
Price Process ◽  
Volatility Index ◽  
Quadratic Interpolation ◽  
Dynamic Estimation ◽  
The Impact

The paper studies methods of dynamic estimation of volatility for financial time series. We suggest to estimate the volatility as the implied volatility inferred from some artificial "dynamically purified" price process that in theory allows to eliminate the impact of the stock price movements. The complete elimination would be possible if the option prices were available for continuous sets of strike prices and expiration times. In practice, we have to use only finite sets of available prices. We discuss the construction of this process from the available option prices using different methods. In order to overcome the incompleteness of the available option prices, we suggests several interpolation approaches, including the first order Taylor series extrapolation and quadratic interpolation. We examine the potential of the implied volatility derived from this proposed process for forecasting of the future volatility, in comparison with the traditional implied volatility process such as the volatility index VIX.

scholarly journals On the Uniqueness of Martingales with Certain Prescribed Marginals

2013 ◽  
Vol 50 (2) ◽  
pp. 557-575
Author(s):  
Michael R. Tehranchi
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Asset Price ◽  
Simple Random Walk ◽  
Option Prices ◽  
Tree Model ◽  
Binomial Tree ◽  
Black Scholes ◽  
Risk Neutral ◽  
Binomial Tree Model

This note contains two main results. (i) (Discrete time) Suppose that S is a martingale whose marginal laws agree with a geometric simple random walk. (In financial terms, let S be a risk-neutral asset price and suppose that the initial option prices agree with the Cox-Ross-Rubinstein binomial tree model.) Then S is a geometric simple random walk. (ii) (Continuous time) Suppose that S=S0eσ X-σ2〈 X〉/2 is a continuous martingale whose marginal laws agree with a geometric Brownian motion. (In financial terms, let S be a risk-neutral asset price and suppose that the initial option prices agree with the Black-Scholes model with volatility σ>0.) Then there exists a Brownian motion W such that Xt=Wt+o(t1/4+ ε) as t↑∞ for any ε> 0.

scholarly journals Size Matters: The Impact of Training Size in Taxonomically-Enriched Word Embeddings

2019 ◽  
Vol 9 (1) ◽  
pp. 252-267
Author(s):  
Alfredo Maldonado ◽  
Filip Klubička ◽  
John Kelleher
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Public Transport ◽  
Crucial Role ◽  
Word Embeddings ◽  
Performance Gains ◽  
Near Synonyms ◽  
The Impact ◽  
Taxonomic Relations ◽  
The Web

AbstractWord embeddings trained on natural corpora (e.g., newspaper collections, Wikipedia or the Web) excel in capturing thematic similarity (“topical relatedness”) on word pairs such as ‘coffee’ and ‘cup’ or ’bus’ and ‘road’. However, they are less successful on pairs showing taxonomic similarity, like ‘cup’ and ‘mug’ (near synonyms) or ‘bus’ and ‘train’ (types of public transport). Moreover, purely taxonomy-based embeddings (e.g. those trained on a random-walk of WordNet’s structure) outperform natural-corpus embeddings in taxonomic similarity but underperform them in thematic similarity. Previous work suggests that performance gains in both types of similarity can be achieved by enriching natural-corpus embeddings with taxonomic information from taxonomies like Word-Net. This taxonomic enrichment can be done by combining natural-corpus embeddings with taxonomic embeddings (e.g. those trained on a random-walk of WordNet’s structure). This paper conducts a deep analysis of this assumption and shows that both the size of the natural corpus and of the random-walk coverage of the WordNet structure play a crucial role in the performance of combined (enriched) vectors in both similarity tasks. Specifically, we show that embeddings trained on medium-sized natural corpora benefit the most from taxonomic enrichment whilst embeddings trained on large natural corpora only benefit from this enrichment when evaluated on taxonomic similarity tasks. The implication of this is that care has to be taken in controlling the size of the natural corpus and the size of the random-walk used to train vectors. In addition, we find that, whilst the WordNet structure is finite and it is possible to fully traverse it in a single pass, the repetition of well-connected WordNet concepts in extended random-walks effectively reinforces taxonomic relations in the learned embeddings.

On the Uniqueness of Martingales with Certain Prescribed Marginals

2013 ◽  
Vol 50 (02) ◽  
pp. 557-575
Author(s):  
Michael R. Tehranchi
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Asset Price ◽  
Simple Random Walk ◽  
Option Prices ◽  
Tree Model ◽  
Binomial Tree ◽  
Black Scholes ◽  
Risk Neutral ◽  
Binomial Tree Model

This note contains two main results. (i) (Discrete time) Suppose that S is a martingale whose marginal laws agree with a geometric simple random walk. (In financial terms, let S be a risk-neutral asset price and suppose that the initial option prices agree with the Cox-Ross-Rubinstein binomial tree model.) Then S is a geometric simple random walk. (ii) (Continuous time) Suppose that S=S 0eσ X-σ2〈 X〉/2 is a continuous martingale whose marginal laws agree with a geometric Brownian motion. (In financial terms, let S be a risk-neutral asset price and suppose that the initial option prices agree with the Black-Scholes model with volatility σ>0.) Then there exists a Brownian motion W such that X t =W t +o(t 1/4+ ε) as t↑∞ for any ε> 0.

Futures and Option Prices After the Stock Market Close: Evidence from the Korean Markets

2008 ◽  
Vol 16 (2) ◽  
pp. 95-125
Author(s):  
Jae Ha Lee ◽  
Sang Soo Kwon
Keyword(s):  
Stock Market ◽  
Trading Volume ◽  
Return Volatility ◽  
Option Prices ◽  
Option Markets ◽  
Option Returns ◽  
Time Zones ◽  
The Impact

In the KOSPI2oo futures and option markets. additional fifteen minutes (15 : 00∼15 개5) after the underlying stock market close are given tor the adjustments of the futures and option positions. During the first five minutes. 15: 00∼15 : 05. a continuous auction trading is made. while the trading at a single clearing price is made for the remaining ten minutes. 15: 05∼15: 15. Previous studies focused on the synchronous trading in terms of transaction time in the analysis of the lead-lag relationship. truncating the futures and option data during 15 : 00∼15 : 15. In this article. we explore how the KOSPI2oo futures and option returns for the extra fifteen minutes impact the next day's KOSPI200 cash returns, We also examine the lead-lag relationship during the reggular trading hours (9 : 00∼15 : 00) and the impact of the cash returns during 14 : 20∼15 : 00 on futures and option returns during 15 : 00∼15: 15. Our main findings are summarized as follows. First. the KOSPI200 futures and option returns during 15 : 00∼15 : 15 lead the close-to-open KOSPI200 cash return, even though the trading volume and return volatility during 15: 00∼15: 15 are lower relative to the regular stock market session (9 : 00∼15: 00). The impact of the futures and option returns on the cash return lasts hlK) minutes and one minute‘ repectively. after the next day open. Second. the option return during the continuous auction trading session (15 : 00∼ 15 : 05) leads the close-to-open cash return. while the futures return of trading at a single clearing price during 15 : 05∼15 : 10 impacts the close-to-open cash return. Third, we found that the lead-lag relationships among the KOSPI200 futures, option, and cash returns are not constant during the reg비ar stock market session‘ In partieular. the impact of the KOSPI200 cash ret un during 14 : 40∼15 : 00 on the futures and option retuns for the 15 : 00∼15: 15 Interval is much stronger. compared with other time zones. Finally. the KOSPI200 cash return during the last ten minutes of trading at a Single clearing price (14 : 50∼15 : 00). significantly impacts the option return during 15: 00∼15: 05. while there is no impact on the futures return (15 : 00∼15: 15).

The impact of net buying pressure on VIX option prices

2019 ◽  
Vol 40 (2) ◽  
pp. 209-227 ◽  
Author(s):  
Yi‐Wei Chuang ◽  
Wei‐Che Tsai ◽  
Ming‐Hung Wu
Keyword(s):  
Option Prices ◽  
The Impact

The Impact of Liquidity on Option Prices

CFA Digest ◽  
2012 ◽  
Vol 42 (1) ◽  
pp. 34-35
Author(s):  
Thomas M. Arnold
Keyword(s):  
Option Prices ◽  
The Impact
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