On Optimal Options Book Execution Strategies with Market Impact

2016 ◽  
Vol 02 (03n04) ◽  
pp. 1750002
Author(s):  
Aymeric Kalife ◽  
Saad Mouti
Keyword(s):  
Implied Volatility ◽  
Option Price ◽  
Spot Price ◽  
Market Impact ◽  
Impact Function ◽  
Optimal Execution ◽  
Execution Strategy ◽  
Variance Risk ◽  
Hamilton Jacobi Bellman ◽  
Mean Variance

We consider the optimal execution of a book of options when market impact is a driver of the option price. We aim at minimizing the mean-variance risk criterion for a given market impact function. First, we develop a framework to justify the choice of our market impact function. Our model is inspired from Leland’s option replication with transaction costs where the market impact is directly part of the implied volatility function. The option price is then expressed through a Black– Scholes-like PDE with a modified implied volatility directly dependent on the market impact. We set up a stochastic control framework and solve an Hamilton–Jacobi–Bellman equation using finite differences methods. The expected cost problem suggests that the optimal execution strategy is characterized by a convex increasing trading speed, in contrast to the equity case where the optimal execution strategy results in a rather constant trading speed. However, in such mean valuation framework, the underlying spot price does not seem to affect the agent’s decision. By taking the agent risk aversion into account through a mean-variance approach, the strategy becomes more sensitive to the underlying price evolution, urging the agent to trade faster at the beginning of the strategy.

scholarly journals A dynamic optimal execution strategy under stochastic price recovery

2015 ◽  
Vol 02 (04) ◽  
pp. 1550025 ◽  
Author(s):  
Masashi Ieda
Keyword(s):  
Order Book ◽  
Market Impact ◽  
Time Step ◽  
Limit Order ◽  
Optimal Execution ◽  
Execution Strategy ◽  
Quasi Variational Inequality ◽  
Finite Time Horizon ◽  
Hamilton Jacobi Bellman ◽  
Optimal Execution Problem

In the present paper, we study the optimal execution problem under stochastic price recovery based on limit order book dynamics. We model price recovery after execution of a large order by accelerating the arrival of the refilling order, which is defined as a Cox process whose intensity increases by the degree of the market impact. We include not only the market order, but also the limit order in our strategy in a restricted fashion. We formulate the problem as a combined stochastic control problem over a finite time horizon. The corresponding Hamilton–Jacobi–Bellman quasi-variational inequality is solved numerically. The optimal strategy obtained consists of three components: (i) the initial large trade; (ii) the unscheduled small trades during the period; (iii) the terminal large trade. The size and timing of the trade is governed by the tolerance for market impact depending on the state at each time step, and hence the strategy behaves dynamically. We also provide competitive results due to inclusion of the limit order, even though a limit order is allowed under conservative evaluation of the execution price.

scholarly journals Optimal Execution considering Trading Signal and Execution Risk Simultaneously

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Yuan Cheng ◽  
Lan Wu
Keyword(s):  
Kernel Function ◽  
Price Impact ◽  
Value Functions ◽  
Feedback Form ◽  
Bellman Equations ◽  
Impact Function ◽  
Optimal Execution ◽  
Dirac Function ◽  
Hamilton Jacobi Bellman ◽  
Optimal Execution Problem

In this paper, we study the optimal execution problem by considering the trading signal and the transaction risk simultaneously. We propose an optimal execution problem by taking into account the trading signal and the execution risk with the associated decay kernel function and the transient price impact function being of generalized forms. In particular, we solve the stochastic optimal control problems under the assumptions that the decay kernel function is the Dirac function and the transient price function is a linear function. We give the optimal executing strategies in state-feedback form and the Hamilton‐Jacobi‐Bellman equations that the corresponding value functions satisfy in the cases of a constant execution risk and a linear execution risk. We also demonstrate that our results can recover previous results when the process of the trading signal degenerates.

scholarly journals Managing investment and liquidity risks for derivatives within a market impact perspective

2017 ◽  
Vol 8 (1) ◽  
pp. 59-73
Author(s):  
Aymeric Kalife
Keyword(s):  
Intrinsic Value ◽  
Market Price ◽  
Market Impact ◽  
Minimal Impact ◽  
Impact Function ◽  
Risk Appetite ◽  
Impact Risk ◽  
High Volatility ◽  
Execution Strategy ◽  
Delta Hedging

The recent period has experienced many instances when market volatility suddenly increased even when there were no well-known fundamental catalysts, as illustrated by the short-lived but sharp transitions from low volatility to high volatility, as many in the last six years as we have had in the prior two decades ‒ increasing evidence that we are in a new volatility-of-volatility regime. Fundamentally, market impact is an illustration of market inefficiency: theories of efficient markets typically expect that investors buy and sell assets based on assessments of their intrinsic value, in contrast with large derivative players who often act based on market price movements which may not be linked to fundamentals. Market impact risk refers to the degree to which large size transactions can be carried out in a timely fashion with a minimal impact on prices. As a result, managing investment and liquidity risks for large players requires introducing an explicit market impact function, and applying to derivatives significantly depends on whether there is or not significant delta hedging activity: in case of no significant delta hedging activity, the risk appetite has significant influence on the optimal execution strategy, while in case of significant delta hedging activity the optimal trading involves feedback hedging effects translating into a modified Black ‒ Scholes hedging strategy.

scholarly journals Can the Implied Information of Options Predict the Liquidity of Stock Market? A Data-Driven Research Based on SSE 50ETF Options

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Hairong Cui ◽  
Jinfeng Fei ◽  
Xunfa Lu
Keyword(s):  
Stock Market ◽  
Risk Premium ◽  
Implied Volatility ◽  
Option Price ◽  
Price Volatility ◽  
Market Liquidity ◽  
Data Driven ◽  
Management Tool ◽  
Variance Risk Premium ◽  
Variance Risk

Liquidity reflects the quality of the market. When the market is short of liquidity, it often causes investors’ trading difficulties and stock price volatility, expanding the investment risk. As a risk management tool, options attract more informed investors to trade because of their flexible design. To explore whether the implied information based on the formation of option price can predict the liquidity of stock market, we take SSE 50ETF options from February 9, 2015, to December 31, 2020, as the research sample. Based on the idea of data-driven approach, we extract the implied information contained in option price, including implied volatility, implied volatility spread, and variance risk premium. Through the regression analysis method, we examine the ability to predict the liquidity of the stock market. The results show that implied volatility spread has the strongest ability to predict the liquidity of the stock market, and it is more significant within 270 days. Implied volatility contains the information about the short-term (120 days) liquidity of the stock market in the future. It shows that implied volatility and implied volatility spread are good indicators to predict stock market liquidity. In contrast, variance risk premium cannot predict the liquidity of stock market. The research conclusion verifies the role of option-implied information in predicting the stock market’s liquidity. By extracting the information of options price, investors and financial regulators can scientifically participate in the financial market under data guidance.

scholarly journals Modified Mean-Variance Risk Measures for Long-Term Portfolios

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 111
Author(s):  
Hyungbin Park
Keyword(s):  
Risk Measures ◽  
Risk Measure ◽  
Investment Strategy ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Volatility Model ◽  
Variance Risk ◽  
Investment Portfolios ◽  
Mean Variance

This paper proposes modified mean-variance risk measures for long-term investment portfolios. Two types of portfolios are considered: constant proportion portfolios and increasing amount portfolios. They are widely used in finance for investing assets and developing derivative securities. We compare the long-term behavior of a conventional mean-variance risk measure and a modified one of the two types of portfolios, and we discuss the benefits of the modified measure. Subsequently, an optimal long-term investment strategy is derived. We show that the modified risk measure reflects the investor’s risk aversion on the optimal long-term investment strategy; however, the conventional one does not. Several factor models are discussed as concrete examples: the Black–Scholes model, Kim–Omberg model, Heston model, and 3/2 stochastic volatility model.

PRICING TIMER OPTIONS: SECOND-ORDER MULTISCALE STOCHASTIC VOLATILITY ASYMPTOTICS

2021 ◽  
pp. 1-19
Author(s):  
XUHUI WANG ◽  
SHENG-JHIH WU ◽  
XINGYE YUE
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Option Price ◽  
Second Order ◽  
Approximation Formula ◽  
Stochastic Volatility Models ◽  
Regular Perturbation ◽  
Volatility Models ◽  
Order Expansion ◽  
High Level

Abstract We study the pricing of timer options in a class of stochastic volatility models, where the volatility is driven by two diffusions—one fast mean-reverting and the other slowly varying. Employing singular and regular perturbation techniques, full second-order asymptotics of the option price are established. In addition, we investigate an implied volatility in terms of effective maturity for the timer options, and derive its second-order expansion based on our pricing asymptotics. A numerical experiment shows that the price approximation formula has a high level of accuracy, and the implied volatility in terms of its effective maturity is illustrated.

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