scholarly journals Detection of arbitrage opportunities in multi-asset derivatives markets

2021 ◽  
Vol 9 (1) ◽  
pp. 439-459
Author(s):  
Antonis Papapantoleon ◽  
Paulo Yanez Sarmiento
Keyword(s):  
Financial Market ◽  
Sufficient Conditions ◽  
Martingale Measure ◽  
No Arbitrage ◽  
Additional Information ◽  
Arbitrage Opportunities ◽  
Equivalent Martingale ◽  
Arbitrage Opportunity ◽  
Derivatives Markets ◽  
Hoeffding Bounds

Abstract We are interested in the existence of equivalent martingale measures and the detection of arbitrage opportunities in markets where several multi-asset derivatives are traded simultaneously. More specifically, we consider a financial market with multiple traded assets whose marginal risk-neutral distributions are known, and assume that several derivatives written on these assets are traded simultaneously. In this setting, there is a bijection between the existence of an equivalent martingale measure and the existence of a copula that couples these marginals. Using this bijection and recent results on improved Fréchet–Hoeffding bounds in the presence of additional information on functionals of a copula by [18], we can extend the results of [33] on the detection of arbitrage opportunities to the general multi-dimensional case. More specifically, we derive sufficient conditions for the absence of arbitrage and formulate an optimization problem for the detection of a possible arbitrage opportunity. This problem can be solved efficiently using numerical optimization routines. The most interesting practical outcome is the following: we can construct a financial market where each multi-asset derivative is traded within its own no-arbitrage interval, and yet when considered together an arbitrage opportunity may arise.

scholarly journals No-Arbitrage Principle in Conic Finance

2020 ◽  
Author(s):  
Mehdi Vazifedan ◽  
Qiji Jim Zhu
Keyword(s):  
Cash Flow ◽  
Financial Models ◽  
Unit Vector ◽  
Martingale Measure ◽  
Financial Model ◽  
No Arbitrage ◽  
Arbitrage Opportunities ◽  
Equivalent Martingale ◽  
Arbitrage Opportunity ◽  
Price Spread

In a one price economy, the Fundamental Theorem of Asset Pricing (FTAP) establishes that no-arbitrage is equivalent to the existence of an equivalent martingale measure. Such an equivalent measure can be derived as the normal unit vector of the hyperplane that separates the attainable gain subspace and the convex cone representing arbitrage opportunities. However, in two-price financial models (where there is a bid-ask price spread), the set of attainable gains is not a subspace anymore. We use convex optimization, and the conic property of this region to characterize the “No-Arbitrage” principle in financial models with the bid-ask price spread present. This characterization will lead us to the generation of a set of price factor random variables. Under such a set, we can find the lower and upper bounds (supper-hedging and sub-hedging bounds) for the price of any future cash flow. We will show that for any given cash flow, for which the price is outside the above range, we can build a trading strategy that provides one with an arbitrage opportunity. We will generalize this structure to any two-price finite-period financial model.

scholarly journals No-Arbitrage Principle in Conic Finance

Risks ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 66
Author(s):  
Mehdi Vazifedan ◽  
Qiji Jim Zhu
Keyword(s):  
Cash Flow ◽  
Financial Models ◽  
Unit Vector ◽  
Martingale Measure ◽  
Financial Model ◽  
No Arbitrage ◽  
Arbitrage Opportunities ◽  
Equivalent Martingale ◽  
Arbitrage Opportunity ◽  
Price Spread

In a one price economy, the Fundamental Theorem of Asset Pricing (FTAP) establishes that no-arbitrage is equivalent to the existence of an equivalent martingale measure. Such an equivalent measure can be derived as the normal unit vector of the hyperplane that separates the attainable gain subspace and the convex cone representing arbitrage opportunities. However, in two-price financial models (where there is a bid–ask price spread), the set of attainable gains is not a subspace anymore. We use convex optimization, and the conic property of this region to characterize the “no-arbitrage” principle in financial models with the bid–ask price spread present. This characterization will lead us to the generation of a set of price factor random variables. Under such a set, we can find the lower and upper bounds (supper-hedging and sub-hedging bounds) for the price of any future cash flow. We will show that for any given cash flow, for which the price is outside the above range, we can build a trading strategy that provides one with an arbitrage opportunity. We will generalize this structure to any two-price finite-period financial model.

scholarly journals The equivalent martingale measure conditions in a general model for interest rates

2005 ◽  
Vol 37 (2) ◽  
pp. 415-434 ◽  
Author(s):  
Kais Hamza ◽  
Saul Jacka ◽  
Fima Klebaner
Keyword(s):  
Interest Rates ◽  
General Model ◽  
Field Model ◽  
Sufficient Conditions ◽  
Martingale Measure ◽  
Equivalent Martingale Measure ◽  
Forward Rates ◽  
No Arbitrage ◽  
Equivalent Martingale ◽  
Integrated Processes

Assuming that the forward rates ftu are semimartingales, we give conditions on their components under which the discounted bond prices are martingales. To achieve this, we give sufficient conditions for the integrated processes ftu=∫0uftvdv to be semimartingales, and identify their various components. We recover the no-arbitrage conditions in models well known in the literature and, finally, we formulate a new random field model for interest rates and give its equivalent martingale measure (no-arbitrage) condition.

scholarly journals The equivalent martingale measure conditions in a general model for interest rates

2005 ◽  
Vol 37 (02) ◽  
pp. 415-434 ◽  
Author(s):  
Kais Hamza ◽  
Saul Jacka ◽  
Fima Klebaner
Keyword(s):  
Interest Rates ◽  
General Model ◽  
Field Model ◽  
Sufficient Conditions ◽  
Martingale Measure ◽  
Equivalent Martingale Measure ◽  
Forward Rates ◽  
No Arbitrage ◽  
Equivalent Martingale ◽  
Integrated Processes

Assuming that the forward rates f t u are semimartingales, we give conditions on their components under which the discounted bond prices are martingales. To achieve this, we give sufficient conditions for the integrated processes f t u =∫0 uf t v dv to be semimartingales, and identify their various components. We recover the no-arbitrage conditions in models well known in the literature and, finally, we formulate a new random field model for interest rates and give its equivalent martingale measure (no-arbitrage) condition.

scholarly journals Spot Market Mechanism Design for the Electricity Market in China Considering the Impact of a Contract Market

Energies ◽  
2019 ◽  
Vol 12 (6) ◽  
pp. 1064 ◽  
Author(s):  
Chen Zhang ◽  
Wei Yan
Keyword(s):  
Electricity Market ◽  
Cost Minimization ◽  
Incentive Compatibility ◽  
Spot Market ◽  
Market Mechanism ◽  
Decomposition Algorithm ◽  
No Arbitrage ◽  
Arbitrage Opportunities ◽  
Arbitrage Opportunity ◽  
The Impact

To promote the reformation of the electricity market in China, a market mechanism that can support collaboration between the contract market and the upcoming spot market was designed in this paper. The focus of this paper was to develop a mechanism to institutionally stabilize the market by way of disciplining market power abuse through limiting arbitrage opportunities generated from multi-markets. To quantitatively describe the arbitrage opportunity, the arbitrage opportunity function (AOF) was defined. Based on inferences of the no-arbitrage principle and the AOF, a cost-based decomposition algorithm for contracts that could improve contract coverage was proposed. The incentive compatible settlement rule for the uncovered generation on the spot market was designed to properly manipulate the arbitrage opportunity. The decomposition algorithm and the settlement rule constituted the designed market mechanism. To verify the applicability and effectiveness of the proposed mechanism, the principles of incentive compatibility, individual rationality, and payment cost minimization were employed to test the designed market mechanism based on the concept of dominant policy equilibrium. This test was conducted on a fictitious case based on the IEEE-14 system. The analysis and results may provide valuable insights on market design in China based on the functional correlation between the contract market and the spot market.

scholarly journals Mean-Variance Hedging Under Additional Market Information

2003 ◽  
Vol 06 (06) ◽  
pp. 613-636 ◽  
Author(s):  
F. Thierbach
Keyword(s):  
Martingale Measure ◽  
Option Prices ◽  
Market Information ◽  
Hedging Strategy ◽  
No Arbitrage ◽  
Finite Set ◽  
The Mean ◽  
Hedging Problem ◽  
Equivalent Martingale ◽  
Mean Variance

In this paper we analyze the mean-variance hedging approach in an incomplete market under the assumption of additional market information, which is represented by a given, finite set of observed prices of non-attainable contingent claims. Due to no-arbitrage arguments, our set of investment opportunities increases and the set of possible equivalent martingale measures shrinks. Therefore, we obtain a modified mean-variance hedging problem, which takes into account the observed additional market information. Solving this we obtain an explicit description of the optimal hedging strategy and an admissible, constrained variance-optimal signed martingale measure, that generates both the approximation price and the observed option prices.

scholarly journals Equivalent Locally Martingale Measure for the Deflator Process on Ordered Banach Algebra

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Boushra Y. Hussein
Keyword(s):  
Banach Algebra ◽  
Sufficient Conditions ◽  
Price System ◽  
Martingale Measure ◽  
Free Lunch ◽  
Equivalent Measure ◽  
Equivalent Martingale ◽  
Necessary And Sufficient ◽  
The Given ◽  
Ordered Banach Algebra

This paper aims at determining the measure of Q under necessary and sufficient conditions. The measure is an equivalent measure for identifying the given P such that the process with respect to P is the deflator locally martingale. The martingale and locally martingale measures will coincide for the deflator process discrete time. We define s-viable, s-price system, and no locally free lunch in ordered Banach algebra and identify that the s-price system C,π is s-viable if and only a character functional ψC≤π exists. We further demonstrate that no locally free lunch is a necessary and sufficient condition for the equivalent martingale measure Q to exist for the deflator process and the subcharacter ϕ∈Γ such that φC=π. This paper proves the existence of more than one condition and that all conditions are equivalent.

A More General One Period Model

2019 ◽  
pp. 27-40
Author(s):  
Tomas Björk
Keyword(s):  
Fundamental Theorem ◽  
Financial Derivatives ◽  
Sample Space ◽  
Martingale Measure ◽  
Finite Sample ◽  
Equivalent Martingale Measure ◽  
No Arbitrage ◽  
Equivalent Martingale ◽  
Absence Of Arbitrage ◽  
Period Model

In this chapter we study a general one period model living on a finite sample space. The concepts of no arbitrage and completeness are introduced, as well as the concept of a martingale measure. We then prove the First Fundamental Theorem, stating that absence of arbitrage is equivalent to the existence of an equivalent martingale measure. We also prove the Second Fundamental Theorem which says that the market is complete if and only if the martingale measure is unique. Using this theory, we derive pricing and hedging formulas for financial derivatives.

scholarly journals WEAK AND STRONG NO-ARBITRAGE CONDITIONS FOR CONTINUOUS FINANCIAL MARKETS

2015 ◽  
Vol 18 (01) ◽  
pp. 1550005 ◽  
Author(s):  
CLAUDIO FONTANA
Keyword(s):  
Financial Markets ◽  
Financial Market ◽  
Asset Price ◽  
Complete Characterization ◽  
Free Lunch ◽  
No Arbitrage ◽  
Price Process ◽  
Arbitrage Opportunity ◽  
No Free Lunch

We propose a unified analysis of a whole spectrum of no-arbitrage conditions for financial market models based on continuous semimartingales. In particular, we focus on no-arbitrage conditions weaker than the classical notions of No Arbitrage opportunity (NA) and No Free Lunch with Vanishing Risk (NFLVR). We provide a complete characterization of the considered no-arbitrage conditions, linking their validity to the characteristics of the discounted asset price process and to the existence and the properties of (weak) martingale deflators, and review classical as well as recent results.

scholarly journals Option Pricing Driven by a Telegraph Process with Random Jumps

2012 ◽  
Vol 49 (3) ◽  
pp. 838-849 ◽  
Author(s):  
Oscar López ◽  
Nikita Ratanov
Keyword(s):  
Option Pricing ◽  
Financial Market ◽  
Option Prices ◽  
Martingale Measures ◽  
Market Models ◽  
Telegraph Process ◽  
Equivalent Martingale Measures ◽  
Hedging Strategies ◽  
Random Jumps ◽  
Equivalent Martingale

In this paper we propose a class of financial market models which are based on telegraph processes with alternating tendencies and jumps. It is assumed that the jumps have random sizes and that they occur when the tendencies are switching. These models are typically incomplete, but the set of equivalent martingale measures can be described in detail. We provide additional suggestions which permit arbitrage-free option prices as well as hedging strategies to be obtained.

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