2006 NTU Finance Conference Bounds and Prices of Currency Cross-Rate Options by San-Lin Chung and Yaw-Huei Wang Comment by: Bing-Huei Lin Department of Business Administration National Taiwan University of Science and Technology December 13, 2006

This paper mainly uses the results of Cherubini, Luciano, and Vechiato (2004), which apply the copula theory to derive the super-replication bounds for an option to exchange one asset for another asset, which are composed of the prices of the univariate options on the two individual exchanged assets. This paper also conducts an intensive empirical examinations, using “confidential” data of OTC option quotes supplied by the trading desk of an (?) investment bank in London. The results show that there exists significant relationships between the market cross-rate option prices and the pricing bounds, and the correlation coefficients.

The research topic is very interesting and important The research topic is very interesting and important. The model is very general. The article is very well written, and the empirical analysis is extensive. The comments are: Cherubini, Luciano, and Vechiato (2004) first applied the copula theory to derive the pricing bound for exchange options. What is the difference between their model and the result of this paper? The authors stress on economic meanings of their pricing bounds because they are portfolios composed of the dollar-rate options and spot dollar rates and are highly informative to the prices of the cross-rate options. In my idea, the economic meaning of pricing bounds means at least they should tell you once the pricing bounds are violated, is it possible or how to arbitrage from that?

The (empirical) pricing bounds are so wide (Table 2 and Figure 1) The (empirical) pricing bounds are so wide (Table 2 and Figure 1). Are they useful practically? The regression analyses show that the pricing bounds have much information in determining the market prices. Since the pricing bounds are simply functions of the prices of options on individual exchange rates, it might be simply the options and/or the dollar exchange rates which contain information for determining the market price of cross-rate options. The equation (A.1) in the appendix. What is the probability distribution techniques? The price of a option on the minimum of two risky assets can be expressed as:

Figure 3 shows risk-neutral moments based on Bakshi et al (2003) Figure 3 shows risk-neutral moments based on Bakshi et al (2003). However, the authors use GB2 (and lognormal mixtures distribution later) to estimate the RND of the two dollar rates. Why not make it consistent? The analysis for inferring option prices through Model 2 Equation (6) is hardly convincing. I am not sure why pricing bounds should provide information on pricing. The authors conclude on this analysis that the results are valuable since this inference provides an effective way to determine prices of cross-rate options when we only have the real-time information of dollar-rate spot and options prices. It is true however you can simply regress the market price of cross-rate options on the dollar-rate options prices and spot prices, and probably can get ever better results!

The analysis of Table 3 is ambiguous since beta is significant may be because the market price of the cross-rate option has reflected the correlation, rather than the pricing bound is correct. You can simply test whether the pricing bounds have information about the correlation or not. Maybe the authors can focus on the explanatory factors, such as (risk-neutral) moments and correlations, and other market factors for the pricing bounds. Equation (6) includes the correlation in the model, because the authors say that no correlation information is included in their pricing bounds. However, according to Proposition 2 of this paper, the pricing bounds do have information about the correlation. To my understanding, the pricing bounds reflect the distribution of the two related dollar-rate including the correlation. With the distribution specified, you have one price solution, and you don’t need pricing bounds.