Option pricing with random risk aversion

Based on a standard general equilibrium economy, we develop a framework for pricing European options where the risk aversion parameter is state dependent, and aggregate wealth and the underlying asset have a bivariate transformed-normal distribution. Our results show that the volatility and the skewness of the risk aversion parameter change the slope of the pricing kernel, and that, as the volatility of the risk aversion parameter increases, the (Black and Scholes) implied volatility shifts upwards but its shape remains the same, which implies that the volatility of the risk aversion parameter does not change the shape of the risk neutral distribution. Also, we demonstrate that the pricing kernel may become non-monotonic for high levels of volatility and low levels of skewness of the risk aversion parameter. An empirical example shows that the estimated volatility of the risk aversion parameter tends to be low in periods of high market volatility and vice-versa.

PENERAPAN AKAD BAI AD-DAYN PADA OBLIGASI SYARIAH DAN SUKUK NEGARA (SURAT BERHARGA SYARIAH NEGARA / SBSN)

In this article, the author tries to provide an in-depth description of the implementation of the Bay Ad-dayn contract on Islamic Bonds and State Sukuk. State Sharia Securities, abbreviated as SBSN or State Sukuk, are State securities issued based on sharia principles, as evidence of the share of participation in SBSN assets, both in rupiah and foreign currencies. In its issuance, SBSN requires the existence of an underlying asset that reflects the ownership share of the assets/benefits/services that forms the basis for the issuance of SBSN. The existence of the underlying asset serves as a real transaction that forms the basis for the issuance of SBSN, and is one of the main aspects that distinguishes the issuance of bonds and sukuk.

Valuation of Insurance Products with Shout Options in a Jump-Diffusion Model

The insurance product with shout options which permit the holders to modify the contract rules is one of the most popular products in European and American markets today. Therefore, it is of great significance to price more precisely. A new mathematical model consisting of a partial differential inequality and constraint conditions is derived for the price of insurance products in a jump-diffusion model. The numerical experiments are performed to analyze the impact of parameters on the insurance product with shout put options, especially for the jump times and the quantities of shout opportunities. The experiment results show that the value of the product is strongly affected by the quantities of shouting opportunities, especially for high values of the underlying asset, while it is only weakly affected for low values. Meanwhile, another meaningful discovery is that the valuation has changed little as the jump times are less than five, while it has shown a sharp increase once the jump times are more than five. Furthermore, the indicator results of course grid errors show that the values of shout put options in the jump-diffusion model are more accurate than those in a Brownian motion.

PENERAPAN AKAD BAI AD-DAYN PADA OBLIGASI SYARIAH DAN SUKUK NEGARA (SURAT BERHARGA NEGARA)

In this article, the author tries to provide an in-depth description of the implementation of the Bay Ad-dayn contract on Islamic Bonds and State Sukuk. State Sharia Securities, abbreviated as SBSN or State Sukuk, are State securities issued based on sharia principles, as evidence of the share of participation in SBSN assets, both in rupiah and foreign currencies. In its issuance, SBSN requires the existence of an underlying asset that reflects the ownership share of the assets/benefits/services that forms the basis for the issuance of SBSN.

Reinforcement Learning for Options Trading

Reinforcement learning has been applied to various types of financial assets trading, such as stocks, futures, and cryptocurrencies. Options, as a novel kind of derivative, have their characteristics. Because there are too many option contracts for one underlying asset and their price behavior is different. Besides, the validity period of an option contract is relatively short. To apply reinforcement learning to options trading, we propose the options trading reinforcement learning (OTRL) framework. We use options’ underlying asset data to train the reinforcement learning model. Candle data in different time intervals are utilized, respectively. The protective closing strategy is added to the model to prevent unbearable losses. Our experiments demonstrate that the most stable algorithm for obtaining high returns is proximal policy optimization (PPO) with the protective closing strategy. The deep Q network (DQN) can exceed the buy and hold strategy in options trading, as can soft actor critic (SAC). The OTRL framework is verified effectively.

Structural Credit Risk Model with Jumps Based on Uncertainty Theory

Traditional finance studies of credit risk structured models are based on the assumption that the price of the underlying asset obeys a stochastic differential equation. However, according to behavioral finance, the price of the underlying asset is not entirely stochastic, and the credibility of financial investors also plays a very important role in asset prices. In this paper we introduce uncertainty theory to describe these credibility of investors and propose a new credit risk structured model with jumps based on the assumption that the underlying asset is described by an uncertain differential equation with jumps. The company default belief degree formula, zero coupon bond value and stock value formula are formulated. Company bond credit spread and credit default swap (CDS) pricing are studied as applications of the proposed model in uncertain markets.

Non-fungible tokens (NFT) and intellectual property: The triumph of the proprietary approach?

Technical methods of intellectual property protection are reviewed and combined in the essay in the discourse of historical development — from man-made signatures of Renaissance artists to non-fungible tokens (NFT). The proliferation of NFTs is analyzed from the point of view of the commercial law: NFTs are discussed as objects that simultaneously have the characteristics of independence and a derivative nature in relation to intellectual property being the underlying digital asset. The self-sufficiency of NFTs as legal objects is provided by their commodity properties, which arise not only from the value of the underlying asset, but from the phenomenon of crystallization of the unique fixed version of the asset in a non-interchangeable and irreproducible token. The derivative nature of NFTs, figuratively correlated with the derivative contracts in financial markets, is manifested in the symbolization of intellectual property as an underlying asset and the loss (in full or in part) of its usual significance for a potential acquirer when placed in an NFT-image. Despite the variety and a specific evolution of legal approaches to the understanding of intellectual property, we can state a long-standing conceptual rejection by legal scholars from the simplest proprietary theories of transferring real rights constructions to intellectual property. However, some absolute property features of the NFTs, ensuring both internal and external legal aspects of the property, raise the question of a new legal life of “proprietarism” in the conditions of digitalization and information capitalism.

Additive logistic processes in option pricing

In option pricing, it is customary to first specify a stochastic underlying model and then extract valuation equations from it. However, it is possible to reverse this paradigm: starting from an arbitrage-free option valuation formula, one could derive a family of risk-neutral probabilities and a corresponding risk-neutral underlying asset process. In this paper, we start from two simple arbitrage-free valuation equations, inspired by the log-sum-exponential function and an $\ell ^{p}$ ℓ p vector norm. Such expressions lead respectively to logistic and Dagum (or “log-skew-logistic”) risk-neutral distributions for the underlying security price. We proceed to exhibit supporting martingale processes of additive type for underlying securities having as time marginals two such distributions. By construction, these processes produce closed-form valuation equations which are even simpler than those of the Bachelier and Samuelson–Black–Scholes models. Additive logistic processes provide parsimonious and simple option pricing models capturing various important stylised facts at the minimum price of a single market observable input.