• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.459-479
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• 2007

Theories related to financial market has received big attention from the statistics community. However, not many courses on the topic are provided in statistics departments. Because the financial theories are entangled with many complicated mathematical and physical theories as well as ambiguously stated financial terminologies. Based on our experience on the topic, we try to explain the rather complicated terminologies and theories with easy-to-understand words. This paper will briefly cover the topics of basic terminologies of derivatives, Black-Scholes pricing idea, and related basic mathematical terminologies.

• The Korean Journal of Applied Statistics
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• v.24 no.4
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• pp.721-733
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• 2011

We consider the state price densities that are implicit in financial asset prices. In the pricing of an option, the state price density is proportional to the second derivative of the option pricing function and this relationship together with no arbitrage principle imposes restrictions on the pricing function such as monotonicity and convexity. Since the state price density is a proper density function and most of the shape constraints are caused by this, we propose to estimate the state price density directly by specifying candidate densities in a flexible nonparametric way and applying methods of regularization under extra constraints. The problem is easy to solve and the resulting state price density estimates satisfy all the restrictions required by economic theory.