Arbitrage Arguments Research Articles

A comparison of machine learning and econometric models for pricing perpetual Bitcoin futures and their application to algorithmic trading

AbstractBitcoin (BTC) perpetual futures contracts are highly leveraged speculative trading instruments with daily market trading of $45 Billion. BTC perpetual futures are derivative contracts, which depend upon the underlying BTC SPOT (current) price. Pricing perpetual futures fairly is hard, using traditional arbitrage arguments, because of the volatile nature of the so called funding rate, which is used as the replacement of risk free rate in the Cryptocurrency market. This work presents a novel technique for pricing BTC futures contracts using conditional volatility and mean models. Intra‐day high‐frequency futures' return volatility and mean are modelled using different ML and econometric techniques. A comparison is made using statistical measures to find the model that best captures the intra‐day conditional mean and volatility. Exponential generalized autoregressive conditional heteroskedasticity is shown to be an almost unbiased predictor of intra‐day volatility, while a constant autoregressive moving average (0, 0) model best captures the conditional mean of the returns. A market directional high frequency trading algorithm is developed using the volatility and mean models. The algorithm first prices the futures contract at some future point of time using the volatility and mean regression models. Next, the slope between the current futures price and the expected price are used to predict the market direction. A long or short position is taken depending upon the expected market direction movement. Extensive back‐testing results show absolute returns of 1500%–8000% depending upon the transaction fees and leverage used. On average, the market direction is predicted correctly 85% of the time by the best model. Finally, the trading technique is market neutral, in that it gives large positive returns, with low SD, in both bull and bear markets.

Merton Miller's Contribution to Modern Finance

This article sums up the research and writings of the University of Chicago's Merton Miller, winner of the 1990 Nobel Prize in Economics, and widely regarded as the “father of modern finance,” in terms of a single governing principle: the role of arbitrage in ensuring the “efficiency” of financial markets and, more generally, the effectiveness of such markets in promoting economic growth and creating social wealth.Starting with the formulation of Proposition I (also known as the capital structure “irrelevance” proposition) with Franco Modigliani in 1958, Miller's research over the next 40 years is seen as applying—with remarkable clarity and consistency—the principle of arbitrage to the study of many aspects of financial markets. Miller's main accomplishment is seen as making arbitrage arguments the cornerstone of modern finance. The arbitrage proof of Proposition I introduced a new standard in finance—namely, that any finding in financial research deserving serious consideration must have the critical property that it cannot represent opportunities for riskless profit by investors. And arbitrage proves to be a constant theme in Miller's writings, from his work in corporate finance to his later studies of financial innovation, derivatives markets, and financial crashes and crises.Having launched and then presided over the transformation of financial studies from a “glorified apprenticeship system” into a scientific discipline, Miller devoted much of the last 15 years of his life to a different, though clearly related undertaking: the defense of financial markets against the attacks of politicians and regulators, as well as businessmen intent on stifling competition—including hostile takeovers. Whether it was the alleged role of the stock index futures markets in the 1987 market crash, the claims of “overleveraging” in the LBOs of the ‘80s, or the derivatives fiascos in the mid‐'90s, Miller was there to provide careful economic analysis of the problems. In the early ‘90s, he explained why the “myopia” of the U.S. stock market was likely to cause far fewer problems than the “hyperopia” induced by regulatory distortions of the Japanese market. And in one of his last speeches, Miller showed that the primary cause of the recent Asian crisis was not “too much reliance on financial markets,” as claimed by politicians and the popular press, but “too little”—in particular, the heavy dependence on bank financing (particularly state‐owned banks) and the failure to develop alternative sources of capital that continues to depress the Japanese economy.

On sovereign default with time-varying interest rates

We extend and refine Aguiar and Amador (2019)'s contraction approach to Eaton and Gersovitz (1981)'s sovereign debt model. In particular, we encompass time-varying interest rates and growth. We show that, when long-term interest rates exceed growth, equilibrium is unique and can be computed via contraction mapping. The method unifies separate branches of literature, showing that the contraction property is the reflection of previous arbitrage arguments based on replication, inspired by Bulow and Rogoff (1989).

Pricing geometric Asian rainbow options under the mixed fractional Brownian motion

We deal with the pricing of geometric Asian rainbow options under the mixed fractional Brownian motion. Based on standard no arbitrage arguments, we obtain a partial differential problem in several independent variables, which we solve by employing suitable changes of variables and analytical results derived in Bos and Ware (2001) and Stulz (1982b). Numerical test-cases are presented in which the pricing formula obtained is applied to geometric Asian rainbow options on two and three underlying assets. Monte Carlo simulations are also performed which confirm the correctness of the proposed closed-form solution.

A consistent stochastic model of the term structure of interest rates for multiple tenors

Starting from the observation that single-currency swap basis spreads contradict classical arbitrage arguments, we construct a framework where this basis arises due to the presence of “roll-over risk.” This risk consists of two components: (1) facing a higher credit spread (e.g. due to a credit downgrade) when rolling over short-term borrowing (2) heightened borrowing costs due to an absence of market liquidity. The model simultaneously fits OIS, interest rate swap and basis swap market quotes. Including CDS market quotes allows the two components of roll-over risk to be explicitly separated. This is highly relevant to the current LIBOR transition, illustrating why alternative benchmarks are fundamentally different from the rates they may be replacing.

On Sovereign Default With Time-Varying Interest Rates

We extend and refine Aguiar and Amador (2019)’s contraction approach to Eaton and Gersovitz (1981)’s sovereign debt model. In particular, we encompass time-varying interest rates and growth. We show that, when long-term interest rates exceed growth, equilibrium is unique and can be computed via contraction mapping. The method unifies separate branches of literature, showing that the contraction property is the reflection of previous arbitrage arguments based on replication, inspired by Bulow and Rogoff (1989).

Perfect Market, Arbitrage, and Value Creation in the MM Proposition

The real contributions of the MM Proposition are its central assumptions of perfect capital markets and the associated arbitrage argument. In this text, we review the perfect market assumptions and no-arbitrage principle. Then, to explain the evolution of the understanding of arbitrage from a deterministic world into an uncertain world, we restate and comment on the proofs of the MM Proposition in current perspectives. With the no-arbitrage principle in mind, we clearly read the circular justification in the MM Proposition and the misleading concept of cost of equity. From the perspective of the distribution of a corporation's value creation, we find that shareholders prefer a maximum degree of debt. However, we believe that the capital structures are mainly constrained by industry characteristics and the market timing of equity and debt financing.

Instantaneous Arbitrage and the CAPM

This paper studies the concept of instantaneous arbitrage in continuous time and its relation to the instantaneous CAPM. Absence of instantaneous arbitrage is equivalent to the existence of a trading strategy which satisfies the CAPM beta pricing relation in place of the market. Thus the difference between the arbitrage argument and the CAPM argument in Black and Scholes (1973) is this: the arbitrage argument assumes that there exists some portfolio satisfying the capm equation, whereas the CAPM argument assumes, in addition, that this portfolio is the market portfolio.

Gradual learning about shocks and the forward premium puzzle

When interest rates are higher in one’s home country than they are abroad, standard arbitrage arguments suggest this signals that the home currency will depreciate in the future. However, empirical evidence has regularly been found to be strongly at odds with this intuition. This is the “forward premium puzzle”. This paper proposes a learning-based explanation for this puzzle. Specifically, we assume economic agents cannot ascertain whether the monetary policy or technology shocks affecting the economy are persistent or transitory but only gradually infer this persistence using Kalman filtering. We embed this information problem in a two-country open-economy DSGE model with nominal rigidities and simulate the model with and without this informational friction. We find that our incomplete information with learning framework, combined with data generating processes dominated by the persistent monetary policy shifts or by slightly distorted beliefs as in Gourinchas and Tornell (2004), lead our artificial data to replicate features of the forward premium puzzle.

Investor sentiment and asset returns: the case of Indian stock market

According to behavioural finance theory, investor sentiment can lead to extreme mispricing of stocks. In this paper we describe the construction of an investor sentiment index for India, an emerging market, to examine the association between sentiment and stock returns. We test whether the sentiment index predicts long-term returns of the stock market, as well as of stock portfolios formed on the basis of size and value characteristics, over the sample period of 2004 to 2016. The sentiment index fails to predict broad market returns, but is inversely associated with the subsequent year's returns of small low-priced stocks, consistent with constrained arbitrage argument of behavioural finance theory and information uncertainty associated with such stocks.

Investor sentiment and asset returns: the case of Indian stock market

According to behavioural finance theory, investor sentiment can lead to extreme mispricing of stocks. In this paper we describe the construction of an investor sentiment index for India, an emerging market, to examine the association between sentiment and stock returns. We test whether the sentiment index predicts long-term returns of the stock market, as well as of stock portfolios formed on the basis of size and value characteristics, over the sample period of 2004 to 2016. The sentiment index fails to predict broad market returns, but is inversely associated with the subsequent year's returns of small low-priced stocks, consistent with constrained arbitrage argument of behavioural finance theory and information uncertainty associated with such stocks.

Novel no-arbitrage conditions for options written on defaultable assets

In this work, we derive an improved lower bound for European-style put options written on defaultable assets. Furthermore, we establish two additional no-arbitrage conditions, one for European-style puts and one for calls, which are tighter than the ones commonly reported in current literature. All of our results are based on static arbitrage arguments and have important implications for constructing arbitrage-free call or put option surfaces. In particular, we point out that the commonly stated conditions required for a call option surface are not always sufficient to generate an arbitrage-free call option surface.

The relative pricing of European dividend futures and their predictive abilities for index returns

We use dividend futures prices to derive a dividend future discount model. Arbitrage arguments postulate that the sum of discounted dividend futures prices should equal the index price, i.e. the sum of discounted dividends. We analyze whether this relation holds and find that the two valuation approaches lead to a different valuation of expected dividends. These observations indicate that dividend futures and index prices seem to provide the investor with different information on future dividends. We further show that the difference in valuation can be used to forecast index returns and show how an investment strategy can exploit this predictability.

Improved lower bounds of call options written on defaultable assets

This article provides an improvedmodel-independent lower bound of European call options written on defaultable assets. On the basis of static arbitrage arguments, improved lower bounds are established, which also depend on the probability of option-implied default. The results are also extended to dividend-paying stocks. Moreover, our findings imply that it is never optimal to exercise certain American call options. Finally, we discuss the implications of our results for constructing an arbitrage-free volatility surface and extracting risk-neutral densities from option prices.

Model-Free Option Prices

In this paper, I have used simple arbitrage argument to derive a dozen of model-free option price properties. In addition to deriving the Greeks under the model-free framework, the results show that first, in contrast to the traditional view, a European call (put) option for a non-dividend-paying asset can also be a European call (put) option for any other non-dividend-paying asset, and every non-dividend-paying asset is also both a European call option and a European put option for any other non-dividend-paying asset. Second, in some cases the time value of the European put option can be negative, and adjust the exercise price of an option can decrease or even erase the time value of the option. I have also used the Arbitrage Theorem under the binomial option pricing model to examine these properties.

Novel No-Arbitrage Conditions for Options Written on Defaultable Assets

Based on the result of Orosi (2014), we derive an improved lower bound for European-style put options written on defaultable assets. Furthermore, we establish two additional no-arbitrage conditions, one for European-style puts and one for calls, which are tighter than the ones commonly reported in current literature. All of our results are based on static arbitrage arguments and have important implications for constructing arbitrage-free call or put option surfaces. In particular, we point out that the commonly stated conditions required for a call option surface are not always sufficient to generate an arbitrage-free call option surface.

Gauge Theory of the Sabr Model

A clear and detailed presentation of the geometric ideas behind the application of the Schwinger-DeWitt heat kernel approach to the solution of the Sabr PDE is given. First we motivate the form of the Sabr PDE by an arbitrage argument. Next a general approach to the solution of the Sabr PDE is formulated and applied to the Normal, Lognormal and General Β case in turn. Some original, more accurate formulae for Sabr prices are derived and compared to the benchmark finite difference solution.

Sistema de Amortização por Múltiplos Contratos: A Falácia do Sistema Francês

By using an arbitrage argument, this article shows that the interpretation of what interest and amortization are at the French system is a fallacy, because it assumes the outstanding balance is refinanced every period at the same rate. Henceforth, it is offered another amortization system that replicates the original cash flow, but with a new interpretation of what is interest or principal in each payment. Depending on the tax regime, this different interpretation may have substantial effects.

Embedded Tax Liabilities and Portfolio Choice

Taxes play an important role in determining after-tax investment risk and returns, but many practitioners still make investment decisions based on pre-tax values. The apparent complexity of dealing with deferred capital gains and the question of how these implied future tax liabilities should be valued are central to this problem. The authors use a simple arbitrage argument to show that a risk-free discount rate is appropriate for calculating the present value of future tax liabilities. This lets analysts adjust risk and returns for effective tax rates and present a more accurate picture to the investor. The results show a taxation-induced preference for holding equities over bonds and a location preference for holding equities in a taxable account and bonds in retirement accounts. These important findings contrast with traditional investment advice that suggests a greater capacity for risk in retirement accounts. <b>TOPICS:</b>Portfolio construction, analysis of individual factors/risk premia, statistical methods

Inflation-Rate Derivatives: From Market Model to Foreign Currency Analogy

In this paper, we establish a market model for the term structure of forward inflation rates based on the risk-neutral dynamics of nominal and real zero-coupon bonds. Under the market model, we can price inflation caplets as well as inflation swaptions with a formula similar to the Black's formula, thus justify the current market practice. We demonstrate how to further extend the market model to cope with volatility smiles. Moreover, we establish a consistency condition on the volatility of real zero-coupon bonds using arbitrage arguments, and with that re-derive the model of Jarrow and Yildirim (2003) with real forward rates based on foreign currency analogy, and thus interconnect the two modeling paradigms.