scholarly journals Liquidity-free implied volatilities: An approach using conic finance

2021 ◽  
pp. 2150041
Author(s):  
Matteo Michielon ◽  
Asma Khedher ◽  
Peter Spreij
Keyword(s):  
European Options ◽  
Security Prices ◽  
Conic Finance ◽  
Risk Neutral ◽  
Theoretical Risk

In this paper, we consider the problem of calculating risk-neutral implied volatilities of European options without relying on option mid prices but solely on bid and ask prices. We provide an approach, based on the conic finance paradigm, that allows to uniquely strip risk-neutral implied volatilities from bid and ask quotes, and that does not require restrictive assumptions. Our methodology also allows to jointly calculate the implied liquidity of the market. The idea outlined in this paper can be applied to calculate other implied parameters from bid and ask security prices as soon as their theoretical risk-neutral counterparts are strictly increasing with respect to the former.

INDEX OPTIONS AND VOLATILITY DERIVATIVES IN A GAUSSIAN RANDOM FIELD RISK-NEUTRAL DENSITY MODEL

2018 ◽  
Vol 21 (04) ◽  
pp. 1850014 ◽  
Author(s):  
XIXUAN HAN ◽  
BOYU WEI ◽  
HAILIANG YANG
Keyword(s):  
Numerical Study ◽  
Gaussian Random Field ◽  
Gaussian Random Fields ◽  
Density Model ◽  
Spot Price ◽  
European Options ◽  
Market Index ◽  
Volatility Derivatives ◽  
Risk Neutral ◽  
Risk Neutral Density

We propose a risk-neutral forward density model using Gaussian random fields to capture different aspects of market information from European options and volatility derivatives of a market index. The well-structured model is built in the framework of the Heath–Jarrow–Morton philosophy and the Musiela parametrization with a user-friendly arbitrage-free condition. It reduces to the popular geometric Brownian motion model for the spot price of the market index and can be intuitively visualized to have a better view of the market trend. In addition, we develop theorems to show how the model drives local volatility and variance swap rates. Hence, volatility futures and options can be priced taking the forward density implied by European options as the initialization input. The model can be accordingly calibrated to the market prices of these volatility derivatives. An efficient algorithm is developed for both simulating and pricing, and a numerical study is conducted using real market data.

scholarly journals Estimation of the Bid-Ask Prices for the European Discrete Geometric Average and Arithmetic Average Asian Options

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Xiankang Luo ◽  
Tao Chen
Keyword(s):  
Law Of One Price ◽  
Asian Options ◽  
European Options ◽  
Quantitative Finance ◽  
Arithmetic Average ◽  
Closed Form Solutions ◽  
Geometric Average ◽  
Conic Finance ◽  
The Law ◽  
Exciting Development

Conic finance is a new and exciting development in quantitative finance, which is widely applied to several topics in finance. The theory of conic finance extends the law of one price to the law of two prices, which yields closed forms for bid-ask prices of European options. In this paper, within the framework of conic finance, we derive effective, explicit, approximate formulas to estimate the bid-ask prices for the European discrete geometric average and arithmetic average Asian options. Finally, we give two examples to demonstrate and validate that the approximate closed-form solutions are efficient and accurate.

scholarly journals Entropic Dynamics of Stocks and European Options

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 765 ◽  
Author(s):  
Mohammad Abedi ◽  
Daniel Bartolomeo
Keyword(s):  
Stock Price ◽  
Inductive Inference ◽  
Planck Equation ◽  
Derivative Securities ◽  
European Options ◽  
Scale Invariant ◽  
No Arbitrage ◽  
Black Scholes ◽  
Risk Neutral ◽  
Log Price

We develop an entropic framework to model the dynamics of stocks and European Options. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. The objective of the paper is to lay down an alternative framework for modeling dynamics. An important information about the dynamics of a stock’s price is scale invariance. By imposing the scale invariant symmetry, we arrive at choosing the logarithm of the stock’s price as the proper variable to model. The dynamics of stock log price is derived using two pieces of information, the continuity of motion and the directionality constraint. The resulting model is the same as the Geometric Brownian Motion, GBM, of the stock price which is manifestly scale invariant. Furthermore, we come up with the dynamics of probability density function, which is a Fokker–Planck equation. Next, we extend the model to value the European Options on a stock. Derivative securities ought to be prices such that there is no arbitrage. To ensure the no-arbitrage pricing, we derive the risk-neutral measure by incorporating the risk-neutral information. Consequently, the Black–Scholes model and the Black–Scholes-Merton differential equation are derived.

scholarly journals Estimation of Ask and Bid Prices for Geometric Asian Options

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Tao Chen ◽  
Kaili Xiang ◽  
Xuemei Luo
Keyword(s):  
Financial Markets ◽  
Equilibrium Price ◽  
Market Liquidity ◽  
Derivative Pricing ◽  
Asian Options ◽  
Explicit Formulas ◽  
Numerical Examples ◽  
Conic Finance ◽  
Risk Neutral ◽  
Bid Prices

Traditional derivative pricing theories usually focus on the risk-neutral price or the equilibrium price. However, in highly competitive financial markets, we observed two prices which are called bid and ask prices; then the unique risk-neutral price fails to hold. In this paper, within the framework of conic finance, we provide a useful approach to evaluate the ask and bid prices of geometric Asian options and obtain the explicit formulas for the ask and bid prices. Finally, numerical examples show that the higher the market liquidity parameter γ, the wider the spread and hence the less the liquidity.

TENOR SPECIFIC PRICING

2012 ◽  
Vol 15 (06) ◽  
pp. 1250043 ◽  
Author(s):  
DILIP B. MADAN ◽  
WIM SCHOUTENS
Keyword(s):  
Difference Equations ◽  
Square Root ◽  
Nonlinear Functions ◽  
Financial Contracts ◽  
Stochastic Difference Equations ◽  
Conic Finance ◽  
Risk Neutral ◽  
Bid Ask Spreads ◽  
Coupon Bond ◽  
Nonlinear Expectations

Observing that pure discount projection curves are now based on a variety of tenors leads us to enquire into the possibility of theoretically deriving tenor specific zero coupon bond prices. The question then also arises on how to construct tenor specific prices for all financial contracts. Noting that in conic finance one has the law of two prices, bid and ask, that are nonlinear functions of the random variables being priced, we model dynamically consistent sequences of such prices using the theory of nonlinear expectations. The latter theory is closely connected to solutions of backward stochastic difference equations. The drivers for these stochastic difference equations are here constructed using concave distortions that implement risk charges for local tenor specific risks. It is then observed that tenor specific prices given by the mid quotes of bid and ask converge to the risk neutral price as the tenor is decreased and liquidity increased when risk charges are scaled by the tenor. Square root tenor scaling can halt the convergence to risk neutral pricing, preserving bid ask spreads in the limit. The greater liquidity of lower tenors may lead to an increase or decrease in prices depending on whether the lower liquidity of a higher tenor has a mid quote above or below the risk neutral value. Generally for contracts with a large upside and a bounded downside the prices fall with liquidity while the opposite is the case for contracts subject to a large downside and a bounded upside.

A COMPARISON OF PRICING KERNELS FOR GARCH OPTION PRICING WITH GENERALIZED HYPERBOLIC DISTRIBUTIONS

2011 ◽  
Vol 14 (05) ◽  
pp. 669-708 ◽  
Author(s):  
ALEXANDRU BADESCU ◽  
ROBERT J. ELLIOTT ◽  
REG KULPERGER ◽  
JARKKO MIETTINEN ◽  
TAK KUEN SIU
Keyword(s):  
Option Pricing ◽  
Discrete Time ◽  
Real Data ◽  
Contingent Claims ◽  
Garch Models ◽  
European Options ◽  
Special Cases ◽  
Risk Neutral ◽  
Pricing Kernels ◽  
Similar Risk

Under discrete-time GARCH models markets are incomplete so there is more than one price kernel for valuing contingent claims. This motivates the quest for selecting an appropriate price kernel. Different methods have been proposed for the choice of a price kernel. Some of them can be justified by economic equilibrium arguments. This paper studies risk-neutral dynamics of various classes of Generalized Hyperbolic GARCH models arising from different price kernels. We discuss the properties of these dynamics and show that for some special cases, some pricing kernels considered here lead to similar risk neutral GARCH dynamics. Real data examples for pricing European options on the S&P 500 index emphasize the importance of the choice of a price kernel.

Security Prices and Business Cycles

1955 ◽  
Vol 11 (1) ◽  
pp. 79-86 ◽  
Author(s):  
Edmund A. Mennis
Keyword(s):  
Business Cycles ◽  
Security Prices

Risk-Neutral and Physical Jumps in Option Pricing

2007 ◽  
Author(s):  
Jian Chen ◽  
Xiaoquan Liu ◽  
Chenghu Ma
Keyword(s):  
Option Pricing ◽  
Risk Neutral
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