Coins With Benefits: On Existence, Pricing Kernel and Risk Premium of Cryptocurrencies

A heat kernel approach is proposed for the development of a novel method for asset pricing over a finite time horizon. We work in an incomplete market setting and assume the existence of a pricing kernel that determines the prices of financial instruments. The pricing kernel is modeled by a weighted heat kernel driven by a multivariate Markov process. The heat kernel is chosen so as to provide enough freedom to ensure that the resulting model can be calibrated to appropriate data, e.g. to the initial term structure of bond prices. A class of models is presented for which the prices of bonds, caplets, and swaptions can be computed in closed form. The dynamical equations for the price processes are derived, and explicit formulae are obtained for the short rate of interest, the risk premium, and for the stochastic volatility of prices. Several of the closed-form models presented are driven by combinations of Markovian jump processes with different probability laws. Such models provide a basis for consistent applications in various market sectors, including equity markets, fixed-income markets, commodity markets, and insurance. The flexible multidimensional and multivariate structure on which the resulting price models are based lends itself well to the modeling of dependence across asset classes. As an illustration, the impact of spiraling debt, a typical feature of a financial crisis, is modeled explicitly, and the contagion effects can be readily observed in the dynamics of the associated asset returns.

Download Full-text

The long-run stability of a small, open economy under crawling peg regime

Acta Oeconomica ◽

10.1556/aoecon.52.2002.1.3 ◽

2002 ◽

Vol 52 (1) ◽

pp. 57-78

Author(s):

S. Çiftçioğlu

Keyword(s):

Exchange Rate ◽

Open Economy ◽

Risk Premium ◽

Small Open Economy ◽

Exchange Rate Policy ◽

Price Stability ◽

Output Stability ◽

Long Run ◽

The Exchange Rate ◽

The Impact

The paper analyses the long-run (steady-state) output and price stability of a small, open economy which adopts a “crawling-peg” type of exchange-rate regime in the presence of various kinds of random shocks. Analytical and simulation results suggest that with the exception of money demand shocks, an exchange rate policy which involves a relatively higher rate of indexation of the exchange rate to price level is likely to lead to the worsening of price stability for all types of shocks. On the other hand, the impact of adopting such a policy on output stability depends on the type of the shock; for policy shocks to the exchange rate and shocks to output demand, output stability is worsened whereas for the shocks to risk premium of domestic assets, supply price of domestic output and the wage rate, better output stability is achieved in the long run.

Download Full-text