A bond is a debt instrument in which an investor loans money to the issuer for a defined period of time and receives coupons paid by the issuer at fixed interest rate. The bond principal will be returned at maturity date. Bonds are usually issued by companies, municipalities, states/provinces and countries to finance a variety of projects and activities

Tim Xiao

Humanities Commons

Fixed Rate BondValuation and RiskFinPricingFixed Rate BondSummary▪ Fixed Rate Bond Introduction▪ The Use of Fixed Rate Bond▪ Valuation: Yield-to-Maturity Approach▪ Valuation: Credit Spread Approach▪ Practical Guide▪ A Real World ExampleFixed Rate BondFixed Rate Bond Introduction▪ A bond is a debt instrument in which an investor loans money to the issuer for a defined period of time.▪ The investor will receive coupons paid by the issuer at a predetermined  interest rate at specified dates before bond maturity.▪ The bond principal will be returned at maturity date.▪ A fixed rate bond is usually a long term paper.▪ Bonds are usually issued by companies, municipalities, states/provinces and countries to finance a variety of projects and activities. Fixed Rate BondThe Use of Fixed Rate Bond▪ Fixed rate bonds generally pay higher coupons than interest rates.▪ An investor who wants to earn a guaranteed interest rate for a specified term can choose fixed rate bonds. ▪ The benefit of a fixed rate bond is that investors know for certain how much interest rate they will earn and for how long.▪ Due to the fixed coupon, the market value of a fixed rate bond is susceptible to fluctuation in interest rate and therefore has a significant interest rate risk.▪ The long maturity schedule and fixed coupon rate offers an investor a solidified return.▪ The real value of a fixed rate bond is also susceptible to inflation rate given its long termFixed Rate BondValuation: Yield-to-Maturity Approach▪ There are two types of bond valuation approaches in the market: yield-to-maturity approach and credit spread approach.▪ The present value of a bond under the yield-to-maturity approach is given by𝑉(𝑡) =෍𝑖=1𝑛𝑐𝑃1 + 𝑦 𝑖+𝑃1 + 𝑦 𝑛wheret – the valuation dateP – the principal amount or face valuey – the yield to maturityc – the coupon ratei – the ith cash flow or coupon from 1 to nFixed Rate BondValuation: Credit Spread Approach▪ The present value of a fixed rate bond under the credit spread model can be expressed as𝑉 𝑡 =෍𝑖=1𝑛𝑐𝑃𝑒− 𝑟𝑖+𝑠 𝑇𝑖 + 𝑃𝑒− 𝑟𝑛+𝑠 𝑇𝑛wheret – the valuation datei – the ith cash flow from 1 to n𝑟𝑖 – the continuous compounded interest rate for period (𝑡, 𝑇𝑖)𝑇𝑖 – the coupon payment date of the ith cash flows – the credit spreadP – the principal amount or face valuec – the coupon rateFixed Rate BondPractical Guide▪ The present value of a bond computed by any pricing models is the dirty price of the bond. To purchase a bond, the buyer pays this dirty price.▪ Although investors pay dirty prices, bonds are typically quoted in terms of clean prices. Dirty Price = Clean Price + Accrued Interest▪ The Yield-To-Maturity Model is a good tool to compute the present value or the fair value of a bond. But it is very difficult to calculate risk, such as term structure sensitivities, that is more important than the fair value in trading, hedging and risk management. Therefore, we introduce the Credit Spread Model for computing both risk and fair value.▪ Intuitively,   𝑒− 𝑟+𝑠 𝑇 can be regarded as a credit risk adjusted discount factor.Fixed Rate BondPractical Guide (Cont)▪ To use the model, one should first calibrate the model price to the market quoted price by solving the credit spread. Comparing to curve construction or calibration for exotic products, the solving here is very simple.▪ After making the model price equal to the market price, one can calculate sensitivities by shocking interest rate curve and credit spread.▪ We use LIBOR curve plus credit spread rather than bond specific curves for discounting because bond specific curves rarely exist in the market, especially issued by small entities. Using LIBOR curve plus credit spread not only accounts for credit/issuer risk but also solves the missing data issue.Fixed Rate BondA Real World ExampleBuy Sell BuyCalendar NYCCoupon Type FixedCurrency USDFirst Coupon Date 11/15/1988Interest Accrual Date 5/15/1988Issue Date 5/16/1988Last Coupon Date 11/15/2017Maturity Date 5/15/2018Settlement Lag 1Face Value 100Pay Receive ReceiveDay Count dcActActPayment Frequency 6MCoupon 0.09125Fixed Rate BondThank YouReference:https://finpricing.com/lib/EqLookback.html

Bond Valuation

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Bond Valuation

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