Tuesday, June 5, 2012

Pricing the probability of a rare event


This article appeared in The Edge in April 2012
By Jasvin Josen
In the previous article, I mentioned the convenience of utilising cat bonds to distribute catastrophic risk out of the insurance industry. The market for cat bonds however has not taken off very satisfactorily and I cited some research that attempted to understand investors’ reluctance to invest in this product. In a nutshell, investors find high loss and highly improbable events, very unsettling.
In this article, I describe the expected loss and some basic thoughts in pricing the probability of a rare event.

Catastrophe Bonds – fear of the unknown?


This article appeared in the Edge in March 2012

By Jasvin Josen

Our planet Earth has experienced a major change since the 1990s. Before the 90s, occurrences of natural disasters like hurricanes, floods, earthquakes and tsunamis were occasional and less severe. After this period however, the occurrence and severity of these catastrophic events increased drastically.
Following this dramatic change, losses caused by catastrophic events have also spiked sharply. Chart 1 illustrates this historical pattern.

Chart 1: World Catastrophe Losses, 1970-2010


Insurance companies have suffered major losses following the protection given against these “Act of God” events. As these events become more common, insurance companies naturally get nervous and tend to increase their rates. Indirectly the burden is passed back to consumers. At the same time, insurance companies also have the other alternative, to “exclude” protection against these disasters, depriving society from protecting their livelihood and trade.

Reinsurance vs. securitisation of catastrophic risk
To avoid a major loss, insurers have traditionally utilised reinsurance contracts. Briefly, this is

Pricing Convertible Securitie


This article appeared in The Edge in Jan 2012

By Jasvin Josen

Convertible securities are traded widely in global debt markets. The most common convertible securities are convertible bonds and convertible preferred stocks. The Convertible Bond (CB) is an equity-linked instrument that gives the holder of the bond the right to convert the bond into a predetermined number of common stock in the future. It is attractive to investors as it provides downside protection of a straight bond with coupons and principal payback at maturity plus the upside return of equities.

Being a hybrid of a bond and equity, the price behaviour of a CB is rather unique. The pricing of CBs is also not very clear-cut. In this article, I describe the features of the CB and its pricing behaviour and illustrate two common pricing methods in the market.

Features of a Convertible Bond
Suppose Company Q issues a convertible bond with a conversion ratio of 25.32 shares. The par value of the bond is $1000. This means that for each $1000 of the par value of this issue that the bondholder exchanges for Company Q’s stock, he will receive 25.32 shares.

The stated conversion price is therefore:
= Par Value of the CB / Conversion Ratio
= $1000 / 25.32
= $39.49

If this CB pays an annual coupon of 6% with a maturity of 5 years, the CB has an investment value. Assuming the risk free discounting rate is 2.5% and the credit spread is zero, the Investment Value of the bond can be derived by discounting its cash flows at the risk free discount rate, as shown in Chart 1.