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 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 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.

Test on the Profit of Pairs Trading Strategy Using KOSPI200 Regular and Mini Options

2018 ◽  
Vol 26 (1) ◽  
pp. 115-151
Author(s):  
Woo–baik Lee
Keyword(s):  
The Other ◽  
Sample Period ◽  
Options Market ◽  
Pairs Trading ◽  
Elapsed Time ◽  
High Profit ◽  
Arbitrage Opportunities ◽  
Arbitrage Trading ◽  
Arbitrage Opportunity ◽  
Price Spread

The KOSPI200 mini option introduced in July 2015 is the derivative of which trading multiplier is reduced to one-fifth of the regular options. This study explored the pairs trading opportunities arising from the price spread between the KOSPI200 regular options and the mini options during the sample period from August 2015 to March 2016 and measured the profits of pairs trading. The main results are summarized as follows. First, the most frequency of pairs trading with high profit was observed for in-the-money options. On the other hands, the frequency of pairs trading opportunities is low and the profit is relatively small for out-of (at)-the money options. Second, for in-the-money options, arbitrage opportunities were captured every three minutes on an average, but the elapsed time between arbitrage opportunity opportunities on out-of-the money options exceeded 10 minutes on average. Third, pairs trading opportunities occur uniformly throughout the day, but profit tends to increase in the afternoon than in the morning. This indicates that price efficiency in options market deteriorates and profit of arbitrage trading with price disparity is higher in the afternoon than that of the morning trading. In addition, the profitability of pairs trading with low liquidity was cross-sectionally higher than those with high liquidity.

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.

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.

Wildcat Capital Investors: Real Estate Private Equity

2017 ◽  
pp. 1-12
Author(s):  
Craig Furfine
Keyword(s):  
Real Estate ◽  
Cash Flow ◽  
Private Equity ◽  
Financial Models ◽  
Cash Flows ◽  
Commercial Real Estate ◽  
Office Building ◽  
Equity Structure ◽  
Financial Model ◽  
Real Estate Investments

Wildcat Capital Investors is a small real estate private equity company. Its MBA intern, Jessica Zaski, is asked to develop a financial model for the purchase of Financial Commons, a 90,000 square foot office building in suburban Chicago. By simple metrics, the property seems to be a good value, but with credit conditions tight, Jessica must consider whether outside investors would be comfortable with the risks of investing in the midst of a severe commercial real estate downturn. Wildcat is designed to give students exposure to both the quantitative and qualitative aspects of investing in commercial real estate through a private equity structure. Beyond the numbers, the case allows for a discussion of the process of finding suitable real estate investments. The importance of the simultaneous negotiations that Wildcat must have with the seller, the lender, and the outside investor can be emphasized.By working through the financial models, students will take a given set of assumptions and analyze the cash flows expected to be received by the equity partners of Financial Commons. With a given deal structure, the students can then model the cash flow to both outside equity investors and Wildcat, learning the mechanics of private equity. The model will allow students to investigate how the variations in the underlying assumptions affect returns to the property and to the investors.

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