This study proposed an optimal model to examine the relationship between the Bitcoin price and six macroeconomic variables – the Bitcoin price, Standard and Poor's 500 volatility index, US treasury 10-year yield, US consumer price index, gold price and dollar index. It also examined the effectiveness of the vector error correction model (VECM) in analyzing the interrelationship among these variables. The authors employed the following approach: first, the authors sampled the period August 2010–February 2022. This is because Bitcoin achieved a market capitalization of more than US$1 tn over this period, gaining market attention and acceptance from retail, corporate and institutional investors. Second, the authors employed a VECM with the six macroeconomic variables. Finally, the authors expanded the long-run equilibrium relationship (time-invariant cointegration)-based VECM to develop a time-varying cointegration (TVC) VECM. The authors estimated the TVC VECM using the Chebyshev polynomial specification based on various information criteria. The results showed that the Bitcoin price can be modeled with the VECM (p = 1, r = 1). The TVC approach generated more explanatory power for Bitcoin pricing, indicating the effectiveness of the approach for modeling the long-run relationship between Bitcoin price and macroeconomic variables.

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This paper examines the pricing of interest rates derivatives such as caps and swaptions in the pricing kernel framework. The underlying state variable is extended to the general infinitely divisible Levy process. For computational purposes, a simple pricing kernel as in Flesaker and Hughston (1996) and Jin and Glasserman (2001) is used. The main contribution or purpose of this paper is to find several proper positive martingales, which is key role of practical applications of the pricing kernel approach with interest rates guarantee to be positive. Particularly, this paper first finds and applies a quite general type of a positive martingale process to pricing interest rate derivatives such as swaptions and range notes in the incomplete market setting. Such interest rate derivatives are hard to find analytic solutions. Consequently, this paper shows that such a choice of the positive martingale in the kernel framework is a promising approach to price interest rate derivatives

Empirical findings on interest rate dynamics imply that short rates show some long memories and non-Markovian. It is well-known that fractional Brownian motion (IBm) is a proper candidate for modelling this empirical phenomena. IBm. however. is not a semimartingale process. For this reason. it is very hard to apply such processes for asset price modelling. Without using Ito formula, we investigate the IBm interest rate theory‘ We obtain a pure discount bond price. and Greeks by using Malllavin calculus.

This paper extracts the factors determining the implied volatility skew movements of KOSPI200 index options by applying PCA (Principal Component Analysis). In particular, we analyze the movement of skew depending on the changes of the underlying asset price. As a result, it turned out that two factors can explain 94.6%~99.8% of the whole movement of implied volatility. The factor1 could be interpreted as ‘parallel shift’, and factor2 as the movement of ‘tilt or slope’. We also find some significant structural changes in the movement of skew after the Financial Crisis. The explanatory power of factor1 becomes more important on the movement of skew in both call and put options after the financial crisis. On the other hand, the influences of the factor2 is less. In general, after financial crisis, the volatility skew has the strong tendency to move in parallel. This implies that the changes in the option price or implied volatility due to the some shocks becomes more independent of the strike prices.