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The effects of price limits and market illiquidity are crucial for pricing derivatives based on some underlying assets traded in the markets with a price limit rule and an illiquidity phenomenon. We develop models to value options for the cases of either the underlying assets encountering price limits and market illiquidity, or when the underlying assets are imposed with price limits and the options themselves show market illiquidity in this paper. The Black–Scholes (1973) model, the Krakovsky (1999) model, and the Ban, Choi, and Ku (2000) model are presented as special cases of our model. Our numerical results show that both the price limit and market illiquidity significantly affect the option values.

The purpose of this chapter is to study the mathematisation of finance – excessive use of mathematical models in finance – which has been widely blamed for the recent financial and economic crisis. We argue that the problem might actually be the financialisation of mathematics, as evidenced by the gradual embedding of branches of mathematics into financial economics. The concept of embeddedness, originally proposed by Polanyi, is relevant to describe the sociological relationship between fields of knowledge. After exploring the relationship between mathematics, finance and economics since antiquity, we find that theoretical developments in the 1950s and 1970s lead directly to this embedding. The key implication of our findings is the realization that it has become necessary to disembed mathematics from finance and economics, and proposes a number of partial steps to facilitate this process. This chapter contributes to the debate on the mathematisation of finance by uniquely combining a historical approach, which chronicles the evolution of the relation between mathematics and finance, with a sociological approach from the perspective of Polyani’s concept of embedding.

We analyze stochastic volatility effects in the context of the bond market. The short rate model is of Vasicek type and the focus of our analysis is the effect of multiple scale variations in the volatility of this model. Using a combined singular-regular perturbation approach we can identify a parsimonious representation of multiscale stochastic volatility effects. The results are illustrated with numerical simulations. We also present a framework for model calibration and look at the connection to defaultable bonds.