arXiv research

Perpetual futures offer leverage without maturity, with prices influenced by funding rates.

Study finds discrepancies in open interest reporting for Bitcoin perpetual swaps.

Derives pricing formulas for perpetual futures contracts.

We develop a trinomial tree model for pricing perpetual derivatives and European options.

The paper explores perpetual contracts in a financial market without arbitrage.

Paper calculates perpetual put option pricing with drawdown cap.

Model simulates Perpetual Futures market with agent behavior.

In complete markets, there are risky assets and a riskless asset. It is assumed that the riskless asset and the risky asset are traded continuously in time and that the market is frictionless. In this paper, we propose a new method for hedging derivatives assuming that a hedger should not always rely on trading existin…

Paper calculates perpetual American put option pricing with drawdown event in Lévy market.

The paper categorizes and analyzes various event-linked perpetual futures contracts.

New option type preserves fungibility by amortizing payments over time.

Researchers calculate the price of a perpetual put option in Lévy models.

Continuous-time random walks are a well suited tool for the description of market behaviour at the smallest scale: the tick-to-tick evolution. We will apply this kind of market model to the valuation of perpetual American options: derivatives with no maturity that can be exercised at any time. Our approach leads to opt…

In this paper we consider the problem of pricing a perpetual American put option in an exponential regime-switching Lévy model. For the case of the (dense) class of phase-type jumps and finitely many regimes we derive an explicit expression for the value function. The solution of the corresponding first passage problem…

Study optimizes funding rates for cryptocurrency perpetual futures to maintain price alignment.

We investigate qualitative and quantitative behavior of a solution of the mathematical model for pricing American style of perpetual put options. We assume the option price is a solution to the stationary generalized Black-Scholes equation in which the volatility function may depend on the second derivative of the opti…

In this paper, we investigate the generalization of the Call-Put duality equality obtained in [1] for perpetual American options when the Call-Put payoff $(y-x)^+$ is replaced by $φ(x,y)$. It turns out that the duality still holds under monotonicity and concavity assumptions on $φ$. The specific analytical form of the …

Closed-form solutions derived for perpetual options under insider models.

The paper values perpetual callable American volatility options using a mean-reverting volatility model.

This paper examines the relationship between Inverse Perpetual Swap contracts, a Bitcoin derivative akin to futures and the margin funding interest rates levied on BitMEX. This paper proves the Heteroskedastic nature of funding rates and goes onto establish a causal relationship between the funding rates and the Bitcoi…

We introduce Hermite fractional financial markets, where market uncertainties are described by multidimensional Hermite motions. Hermite markets include as particular cases financial markets driven by multivariate fractional Brownian motion and multivariate Rosenblatt motion. Conditions for no-arbitrage and market comp…

Perpetual American options are financial instruments that can be readily exercised and do not mature. In this paper we study in detail the problem of pricing this kind of derivatives, for the most popular flavour, within a framework in which some of the properties |volatility and dividend policy| of the underlying stoc…

A new framework assesses liquidity risk in perpetual futures exchanges.

The paper tackles dynamic collateral control for spot-perpetual basis trading in decentralized finance.

American options are financial instruments that can be exercised at any time before expiration. In this paper we study the problem of pricing this kind of derivatives within a framework in which some of the properties --volatility and dividend policy-- of the underlaying stock can change at a random instant of time, bu…

A variational inequality for pricing the perpetual American option and the corresponding difference equation are considered. First, the maximum principle and uniqueness of the solution to variational inequality for pricing the perpetual American option are proved. Then the maximum principle, the existence and uniquenes…

PDLPs reduce borrowing costs for perpetual futures traders.

Adaptive pricing framework for perpetual contracts using liquidity curves and oracles.

It is well known how to determine the price of perpetual American options if the underlying stock price is a time-homogeneous diffusion. In the present paper we consider the inverse problem, that is, given prices of perpetual American options for different strikes, we show how to construct a time-homogeneous stock pric…

Two new methods for option pricing without or with a riskless asset.

A pricing formula for discount bonds, based on the consideration of the market perception of future liquidity risk, is established. An information-based model for liquidity is then introduced, which is used to obtain an expression for the bond price. Analysis of the bond price dynamics shows that the bond volatility is…

We analyze and calculate the early exercise boundary for a class of stationary generalized Black-Scholes equations in which the volatility function depends on the second derivative of the option price itself. A motivation for studying the nonlinear Black Scholes equation with a nonlinear volatility arises from option p…

It is well known that in models with time-homogeneous local volatility functions and constant interest and dividend rates, the European Put prices are transformed into European Call prices by the simultaneous exchanges of the interest and dividend rates and of the strike and spot price of the underlying. This paper inv…

This paper optimizes perpetual contract liquidity by accounting for funding rates.

Agent optimizes perpetual contract liquidation with transaction costs and risk.

This study examines how DEXs impact traders' behavior in perpetual futures contracts.

This paper designs a new on-chain option that amortizes perpetual options for blockchain environments.

Study finds Binance's tether-margined contracts significantly impact bitcoin volatility.

Study finds optimal boundaries for hedging a perpetual American put option.

We prove that the perpetual American put option price of level dependent volatility model with compound Poisson jumps is convex and is the classical solution of its associated quasi-variational inequality, that it is $C^2$ except at the stopping boundary and that it is $C^1$ everywhere (i.e. the smooth pasting conditio…

TWM doesn't reduce delta in PDLPs, proving impossibility.

This paper examines the valuation of a generalized American-style option known as a Game-style call option in an infinite time horizon setting. The specifications of this contract allow the writer to terminate the call option at any point in time for a fixed penalty amount paid directly to the holder. Valuation of a pe…

AutoQuant addresses cryptocurrency backtesting fragility by modeling execution costs and improving strategy selection.

Optimizes Ethena's yield strategy by controlling stETH and ETH futures positions.

We extend the classical Cox-Ross-Rubinstein binomial model in two ways. We first develop a binomial model with time-dependent parameters that equate all moments of the pricing tree increments with the corresponding moments of the increments of the limiting Itô price process. Second, we introduce a new trinomial model i…

Panoptic trades options without oracles on Ethereum.

One of the main obstacles regarding Barky Emery curvature on graphs is that the results require a global uniform lower curvature bounds where no exception sets are allowed. We overcome this obstacle by introducing the perpetual cutoff method. As applications, we prove gradient estimates only requiring curvature bounds …

The paper proves ADL mechanisms face a trilemma and optimizes them for fairness, revenue, and exchange solvency.