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Strict local martingales may admit arbitrage opportunities with respect to the class of simple trading strategies. (Since there is no possibility of using doubling strategies in this framework, the losses are not assumed to be bounded from below.) We show that for a class of non-negative strict local martingales, the strong Markov property implies the no arbitrage property with respect to the class of simple trading …
We fully characterize the absence of Butterfly arbitrage in the SVI formula for implied total variance proposed by Gatheral in 2004. The main ingredient is an intermediary characterization of the necessary condition for no arbitrage obtained for any model by Fukasawa in 2012 that the inverse functions of the -d1 and -d2 of the Black-Scholes formula, viewed as functions of the log-forward moneyness, should be increasi…
We introduce a trade strategy representation theorem for performance measurement and portable alpha in high frequency trading, by embedding a robust trading algorithm that describe portfolio manager market timing behavior, in a canonical multifactor asset pricing model. First, we present a spectral test for market timing based on behavioral transformation of the hedge factors design matrix. Second, we find that the t…
In fixed income sector, the yield curve is probably the most observed indicator by the market for trading and fifinancing purposes. A yield curve plots interest rates across different contract maturities from short end to as long as 30 years. For each currency, the corresponding curve shows the relation between the level of the interest rates (or cost of borrowing) and the time to maturity. For example, the U.S. doll…
Leveraged ETFs (L-ETFs) are exchange-traded funds that achieve price movements several times greater than an index by holding index-linked futures such as Nikkei Stock Average Index futures. It is known that when the price of an L-ETF falls, the L-ETF uses the liquidity of futures to limit the decline through arbitrage trading. Conversely, when the price of a futures contract falls, the futures contract uses the liqu…
We derive the arbitrage gains or, equivalently, Loss Versus Rebalancing (LVR) for arbitrage between \textit{two imperfectly liquid} markets, extending prior work that assumes the existence of an infinitely liquid reference market. Our result highlights that the LVR depends on the relative liquidity and relative trading volume of the two markets between which arbitrage gains are extracted. Our model assumes that tradi…
The no Butterfly arbitrage domain of Gatheral SVI 5-parameters formula for the volatility smile has been recently described. It requires in general a numerical minimization of 2 functions altogether with a few root finding procedures. We study here the case of some sub-SVIs (all with 3 parameters): the Symmetric SVI, the Vanishing Upward/Downward SVI, and SSVI, for which we provide an explicit domain, with no numeric…
The standard approach for compensating liquidity providers on many decentralized exchanges (DEX) for serving as counter-party to swaps is through charging a small percentage of fees. The expected payoff from the cash flow of this mode of market making has yet to be mathematically formulated in terms of volatility in the existing literature. We provide here a preliminary derivation of the payoff formula, by making the…
In the context of large financial markets we formulate the notion of \emph{no asymptotic free lunch with vanishing risk} (NAFLVR), under which we can prove a version of the fundamental theorem of asset pricing (FTAP) in markets with an (even uncountably) infinite number of assets, as it is for instance the case in bond markets. We work in the general setting of admissible portfolio wealth processes as laid down by Y.…
The purpose of this paper is two-fold. First is to extend the notions of an n-dimensional semimartingale and its stochastic integral to a piecewise semimartingale of stochastic dimension. The properties of the former carry over largely intact to the latter, avoiding some of the pitfalls of infinite-dimensional stochastic integration. Second is to extend two fundamental theorems of asset pricing (FTAPs): the equivalen…
We extend a linear version of the liquidity risk model of Cetin et al. (2004) to allow for price impacts. We show that the impact of a market order on prices depends on the size of the transaction and the level of liquidity. We obtain a simple characterization of self-financing trading strategies and a sufficient condition for no arbitrage. We consider a stochastic volatility model in which the volatility is partly c…
Most insurance contracts are inherently linked to financial markets, be it via interest rates, or -- as hybrid products like equity-linked life insurance and variable annuities -- directly to stocks or indices. However, insurance contracts are not for trade except sometimes as surrender to the selling office. This excludes the situation of arbitrage by buying and selling insurance contracts at different prices. Furth…
We apply Geometric Arbitrage Theory to obtain results in mathematical finance for credit markets, which do not need stochastic differential geometry in their formulation. We obtain closed form equations involving default intensities and loss given defaults characterizing the no-free-lunch-with-vanishing-risk condition for corporate bonds, as well as the generic dynamics for credit market allowing for arbitrage possib…
We consider the fundamental theorem of asset pricing (FTAP) and hedging prices of options under non-dominated model uncertainty and portfolio constrains in discrete time. We first show that no arbitrage holds if and only if there exists some family of probability measures such that any admissible portfolio value process is a local super-martingale under these measures. We also get the non-dominated optional decomposi…
Automated market makers (AMMs) are a new type of trading venues which are revolutionising the way market participants interact. At present, the majority of AMMs are constant function market makers (CFMMs) where a deterministic trading function determines how markets are cleared. Within CFMMs, we focus on constant product market makers (CPMMs) which implements the concentrated liquidity (CL) feature. In this thesis we…
A new modelling approach that directly prescribes dynamics to the term structure of VIX futures is proposed in this paper. The approach is motivated by the tractability enjoyed by models that directly prescribe dynamics to the VIX, practices observed in interest-rate modelling, and the desire to develop a platform to better understand VIX option implied volatilities. The main contribution of the paper is the derivati…
In this work we consider three problems of the standard market approach to pricing of credit index options: the definition of the index spread is not valid in general, the usually considered payoff leads to a pricing which is not always defined, and the candidate numeraire one would use to define a pricing measure is not strictly positive, which would lead to a non-equivalent pricing measure. We give a general mathem…
We study superhedging of contingent claims with physical delivery in a discrete-time market model with convex transaction costs. Our model extends Kabanov's currency market model by allowing for nonlinear illiquidity effects. We show that an appropriate generalization of Schachermayer's robust no arbitrage condition implies that the set of claims hedgeable with zero cost is closed in probability. Combined with classi…