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The purpose of this paper is to outline a pricing formula for the valuation of catastrophic (CAT) bonds as applied to multiple trigger drought risks in Kenya.

The valuation model is designed around the multiple triggers of the Mexican Catastrophe bonds, but the valuation model is based on Jarrow’s (2010) closed form CAT Bond Pricing model. The authors outline the model structure, the multiple tranches with rainfall triggers, and simulate the model using Monte Carlo methods. Data input was synthesized from historical rainfall data in Kenya’s Moyale region as well as prevailing LIBOR and rates and conventional coupons.

The authors compute the valuation model using Monte Carlo techniques. The authors found the pricing method to be robust and consistent under various parameter settings including trigger levels, time after launch, recovery rates, coupon spreads, and zero coupon curves. For example the higher the trigger rates, the lower will be the bond price at issue. With 50 percent recovery the CAT bond at issue would be around $702 with a high triggers and 976 with low triggers, but the valuation changes with parameters.

As far as the authors know the use of multiple trigger CAT bonds has been very limited in practice. The valuation formula and methods outlined in this paper show how CAT bonds can be effectively designed to address CAT covariate risks in developing agricultural economies.

This paper examines CAT bonds to investigate multi-trigger rainfall risks in Kenya. The paper shows how CAT bonds can be designed to meet specific and CAT risks. Using Jarrow’s (2010) closed form solution this paper is one of the first to apply it to the macro-management of agricultural risks.

This paper determines a simple transformation that nearly linearizes the bond price formula. The transformed price can be used to derive a highly accurate approximation of the change in a bond price resulting from a change in interest rates.

A logarithmic transformation exactly linearizes the price function for a zero coupon bond and a reciprocal transformation exactly linearizes the price function for a perpetuity. A power law transformation combines aspects of both types of transformations and provides a superior approximation of the bond price sensitivity for both short-term and long-term bonds.

It is demonstrated that the new formula, based on power-law transformation, is a much better approximation than either the traditional duration-convexity approximation and the more recently developed approximations based on logarithmic transformation of the price function.

The new formula will be used by risk managers to perform stress-testing on bond portfolios. The new formula can easily be inverted, making it possible to relate the distribution of prices (which are observable in the market) to the distribution of yields (which are numerical solutions that are not directly observable).

In February 2015, Suzlon had just completed its financial and asset restructuring, following financial default after rapid growth through debt financed acquisitions in the financial boom ending in 2008. The restructuring resulted in a significant decrease in the promoter's equity stake. Suzlon now has to decide how to respond to an offer by the DilipSanghvi Group, promoters of Sun Pharma, to acquire a large equity stake in Suzlon for Rs. 1,800 crore. If Suzlon were to accept the offer then both the existing promoters and the DilipSanghvigroup would have the same stake of about 22% each. The case will help students examine the need to align financing and business strategy on the same plane. It will also help them understand details about restructuring of financial and business strategy in the face of financial distress.

In this chapter, we define the “inflation forward rates” based on arbitrage arguments and develop a dynamic model for the term structure of inflation forward rates. This new model can serve as a framework for specific no-arbitrage models, including the popular practitioners’ market model and all models based on “foreign currency analogy.” With our rebuilt market model, we can price inflation caplets, floorlets, and swaptions with the Black formula for displaced-diffusion processes, and thus can quote these derivatives using “implied Black's volatilities.” The rebuilt market model also serves as a proper platform for developing models to manage volatility smile risks.

Through this chapter, we hope to correct two major flaws in existing models or with the current practices. First, a consumer price index has no volatility, so models based on the diffusion of the index are essentially wrong. Second, the differentiation of models based on zero-coupon inflation-indexed swaps and models based on year-on-year inflation-indexed swaps is unnecessary, and the use of “convexity adjustment,” a common practice to bridge models that are based on the two kinds of swaps, is redundant.

The case highlights the ambitious growth strategy of Suzlon, an Indian company specializing in non-conventional (wind) energy. In 2007, Suzlon announced the acquisition of REpower of Germany, one of the top wind power companies in the world. It issued zero coupon and coupon bearing foreign currency (US dollar) convertible bonds (FCCB) amounting to $760 million to finance the acquisition. These bonds were listed in Singapore. Due to deteriorating business conditions the company experienced a sharp decline in profitability and stock price resulting in a debt overhang. At the same time, the Indian rupee depreciated from INR44 to INR55 leading to losses on largely unhedged, foreign currency coupon payments. The company had to restructure its capital structure to escape bankruptcy. Since FCCB holders did not agree to restructure the terms of the instrument, the company had to turn to senior lenders to restructure debt. Eventually Suzlon had to sell-off REpower to reduce leverage.

The case is based on interviews of market intermediaries and published information. The information relating to the restructuring has been taken from the information statement filed with the Securities Exchange Board of India and the Stock Exchanges. The timeline of events were constructed from the information available in company press releases. Financial statements and other details are from the documents filed with the regulators and supplemented with the information available in Prowess database. The stock price and stock market index data are from the websites of Bombay Stock Exchange and the National Stock Exchange of India. Exchange rates, inflation and interest rates have been taken from Bloomberg and the Reserve Bank of India website. Valuation inputs like multiples are from Prowess database and security analyst reports. Sources of information are documented appropriately in the case and instructor’s manual. Although we interviewed the investment bankers involved in the restructuring we have not included any private information in the case to preserve confidentiality.

This case can be used in a corporate finance course or in a module on debt restructuring in a corporate restructuring course or in the financing module in an advanced corporate finance course or in an International Finance course. It can also be used to teach an integrated approach to valuation and financing in a valuation course.

The case highlights the rationale for issuing FX convertible debt, parity conditions in international finance and the use of alternate valuation models.

The purpose of this paper is to estimate the effects of liquidity on corporate bond spreads.

Using a systematic liquidity factor extracted from the yield spreads between on- and off-the-run Treasury issues as a state variable, the authors jointly estimate the default and liquidity spreads from corporate bond prices.

The authors find that the liquidity factor is strongly related to conventional liquidity measures such as bid-ask spread, volume, order imbalance, and depth. Empirical evidence shows that the liquidity component of corporate bond yield spreads is sizable and increases with maturity and credit risk. On average the liquidity spread accounts for about 25 percent of the spread for investment-grade bonds and one-third of the spread for speculative-grade bonds.

The results show that a significant part of corporate bond spreads are due to liquidity, which implies that it is not necessary for credit risk to explain the entire corporate bond spread.

The results show that returns from investments in corporate bonds represent compensations for bearing both credit and liquidity risks.

It is a novel approach to extract a liquidity factor from on- and off-the-run Treasury issues and use it to disentangle liquidity and credit spreads for corporate bonds.