Non Quanto Convertible Bond
A convertible bond can also be called by the issuer or redeemed (put) by the bondholder, dependent on the contract specifications. As to the bond itself, it can be a fixed rate bond, or a floating rate bond.
In a non-quanto convertible bonds, the spot stock price in foreign currency is converted into an amount in domestic currency using the spot exchange rate. This amount is then adjusted by the current value of predicted future discrete dividends, measured in domestic currency. The domestic risk-free interest rate is employed as the drift rate for the translated stock.
Let be the stock price measured in a foreign currency. Let be the exchange rate, quoted in domestic currency per one unit of foreign currency. A non-quanto convertible bond allows the holder of the bond converts the bond to the stock at any time u after the specified conversion start date, with the stock value equivalent to . The coupons and notional of the bond are measured in domestic currency.
If a conversion cash is specified in the convertible bond contract, at conversion, the conversion value to the investor is
Once the fair value of the convertible bond is calculated, where t is the value date, a semi-annually compounded yield-to-maturity value y can be computed such that
A convertible bond can be priced using a lattice tree. The most common method to price a convertible bond is so called “risky discount method, where the bond value at each node in the tree is decomposed into an equity component and a bond component. When an asset swap or a default swap is used to hedge the convertible bond, the bond price can be priced.
It is known that prices obtained using lattice trees are oscillated with the number of time steps. A semi-continuous tree model is enhancement to the lattice tree, which can produce prices converging smoothly as the number of time steps grows. Nevertheless, prices from simple lattice trees and semi-continuous trees will convergence to the true values eventually when the number of time steps is sufficiently large.
References:
ResearchGate non quanto convertible pdf