Casualty Reinsurance Seminar, June 7th, 2004, Boston June 7, 2004 “ “ Cat Bond Pricing Using Cat Bond Pricing Using Probability Transforms Probability Transforms ” ” published in published in Geneva Papers, 2004 Geneva Papers, 2004 Shaun Wang, Ph.D., FCAS
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Casualty Reinsurance Seminar, June 7th, 2004, Boston
June 7, 2004
““Cat Bond Pricing Using Probability Cat Bond Pricing Using Probability TransformsTransforms””published in published in Geneva Papers, 2004Geneva Papers, 2004
Shaun Wang, Ph.D., FCAS
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Shaun Wang, June 2004
What is CAT bond?
A high-yield debt instrument: if the issuer (insurance company) suffers a loss from a particular predefined catastrophe, then the issuer's obligation to pay interest and/or repay the principal is either deferred or forgiven.
Covered events: CA Earthquake, Japan Earthquake, FL Hurricane, EU Winter Storm; Multi-Peril & Multi-territory
Actual-dollar trigger or Reference-index trigger
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Shaun Wang, June 2004
Why CAT bond?
For bond issuers: Alternative source of capital/capacity for insurance
companies with large risk transfer needs
Not subject to the risk of non-collectible reinsurance
For investors: High yield coupon rate CAT bond performance is not closely correlated with
the stock market or economic conditions.
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Shaun Wang, June 2004
Example of Cat-bond transactions(Data Source: Lane Financial LLC)
Cat bond Transaction
Probability of First $
Loss
Probability of Last $
Loss
Expected Loss given
default
Yields Spread Over
LIBORAtlas Re A 0.0019 0.0005 0.5789 2.74%Atlas Re B 0.0029 0.0019 0.7931 3.75%Atlas Re C 0.0547 0.019 0.5923 14.19%
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Shaun Wang, June 2004
State of the Cat-bond Market
In the past, unfamiliar class of assets to investors, led to limited number of transactions
Phenomenal performance of CAT bond portfolios, led to recent surge of interest by institutional investors
Cat Bond Market Grew 42% in 2003 Total bond issuance $1.73 billion Reduced cost of issuing (coupon interest and
transaction costs)
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Shaun Wang, June 2004
Cat-bond offers a laboratory for reconciliation of pricing approaches Capital market pricing is forward-looking:
prices incorporate all available information
No-arbitrage pricing (Black-Scholes Theory)
Actuarial pricing is back-forward looking Using historical data to project future costs
Explicit adjustments for risk
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Shaun Wang, June 2004
Financial World
Black-Schole-Merton theory for pricing options and corporate credit default risks
A common measure for fund performance is the Sharpe ratio: ={ E[R] r }/[R], the excess return per unit of volatility
Use 2-factor Wang transform to fit historical default probability & yield spread by bond rating classes
Compare the fitted parameters for “corporate bond” versus “CAT-bond”
parameters are similar,
“CAT-bond” has lower Student-t degrees-of-freedom,
In 1999, CAT-bond offered more attractive returns for the risk than corporate bonds
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Shaun Wang, June 2004
Cat bond vs. Corporate Bond (before)
Before Sept. 11 of 2001 fund managers were less familiar (or comfortable) with the cat bond asset class.
Fund managers were reluctant to expose themselves to potential career risks, since they would have difficulties in explaining losses from investing in cat bonds, instead of conventional corporate bonds.
At that time, because of investors’ weak appetite for cat bonds, cat bonds issuers had to offer more attractive yields than corporate bonds with comparable default frequency & severity.
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Shaun Wang, June 2004
Cat bond vs. Corporate Bond (after)During 2002-3, fund managers' interest in cat bond has growth significantly, due to superior performance of the cat bond class. They now complaint about not having enough cat bond issues to feed their risk appetite.
In the same time period, the perceived credit risk of corporate bonds increased, in tandem with the general broader market. Investors began to value more the benefit of low correlation between cat bond and other asset classes.
It has been reported that the yields spreads on cat bonds have tightened while the yields spreads on corporate bonds have widened (cross over) – Polyn April 2003.