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Let $V(t, r_t, S_t)$ be the convertible bond price at time $t$, where \begin{align*} dS_t &= S_t(r_t dt + \sigma dW_t^1)\\ dr_t &=\kappa(\theta-r_t)dt+\Sigma dW_t^2, \end{align*} and where $\{W_t^1, \, t\ge 0\}$ and $\{W_t^2, \, t\ge 0\}$ are two standard Brownian motions with $d\langle W^1, W^2\rangle_t = \rho dt$. Then, \begin{align*} &\ dV(t, ...

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The major difference is that the equity option embedded in a convertible bond is not detachable from the convert, so that you have to value the bond and the embedded option together. If you want to make a direct comparison with a detachable warrant, you can think of the the embedded option in a convertible bond as having a strike price equal to the value of ...

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Both statements are correct. A warrant allows a holder to BUY a stock at a set price. Because there is a specific price, all that is needed is CASH to get the stock. As such, the warrant can be separated from the bond, and someone else could use it. As a result, it is valued separately from an accounting perspective. A convertible bond, on the other hand, ...

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NIM5 , will pull up equity linked securities and you can input a date range if you toggle the Issue History radio button.

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You have a conversion ratio of $100/12.1 \approx 8.26$, so the convertibility is an option on about 8 underlying stocks and the delta scales accordingly. I'm not familiar about the way it's quoted, though. Did you expect it to be the delta for one unit of stock?

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The maturity of an investment is the end date of the contract. For example, you can buy a bond that pays P*(1+r) one year from now, where P is the price you pay, r is the interest rate, and the day on which it expires (one year from today) is the expiration date. Another example, in the case of options contracts, you buy a contract that gives you the ...

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A friend gave me the following reply in terms of dynamic hedging and portfolio management: Quantitative justification Pricing models for a CB are based on holding the CB hedged with a short equity position. The combined portfolio has zero delta. However, it has positive gamma. To see this, consider that delta increases when the probability of conversion ...

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That company is probably traded on the Hungarian stock exchange in Hungarian forint. You would have to multiply the stock price by the euro/forint rate to find parity. Note that in this case, the bond has a huge coupon (Euribor+5.5%) after the "call date", effectively forcing the call and making the bond a 4% maturing in 2016. There's no real point to ...

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If you are asking whether it is possible to price path-dependent American options in tree based models, the short answer is yes. You simply construct your tree/grid and evaluate the rules in each node (analogous to what you would do in your MC simulations). These rules can be arbitrarily complex. Note, however, that you can only evaluate them at a discrete ...

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Unfortunately, convertible bonds are quite complex so you don't have simple formulas or approaches as with vanilla bonds. However, this does not mean you are powerless. You can follow different approaches, for instance: 1) If you have a pricing model for the convertible, you can use the finite difference method (or other techniques) to get any sensitivity. ...

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The Theory of Corporate Finance is an academic field that tries to explain theoretically why companies issue the kinds of securities they do. The simplest company, a steady state business that earns say X a year growing at y% a year could be financed with equity and (optionally) debt alone. How then do we explain the great variety of instruments that real ...

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I have recently released a Python financial library called FinancePy. It has a convertible bond model implementation. It is still in beta so may have some bugs but you are welcome to try it out. It also uses Numba so it is fast and you can look through to the actual Python code. The github is at https://github.com/domokane/FinancePy Here is an example ...

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I assume below because if now AirBnb is at 19, investor will just convert at 18 and make $1 immediately? Wrong, that call option (the warrant part of the deal) has intrinsic value even if the current share price is above the strike. Else all investors would exercise their convertible bonds as soon as the spot goes above the strike. Maybe those investors ... 1 OK, here is what I think. (But you should ask for advice from others in this forum or elsewhere). You computed$\frac{dC}{dK}$(the dual delta) by a discrete approximation. The result is negative and this is correct (it is negative for a Call and Positive for a Put). In the case of a European Call it is given by the formula$-e^{-r T}N(d_2)$. (See here for ... 1 Here's my$1/50. Please be free to raise any suggestions. Don't regress the split cashflows respectively as in TF, just regress the whole continuation value instead. When the bond is in the callable period, we'll have to use all paths; Otherwise, when in the convertible period, only consider the paths where conversion value > straight bond value (or should ...

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The usual approach to deal with path dependency in finite differences/lattices solvers is to capture the path dependency trough one or more auxiliary variable(s) that make the problem non path dependent in the augmented space, and to discretize along these auxiliary variable(s). For instance that's easily done for asian options where the path dependency is ...

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Negative yields will typically be negative do to the value of option (conversion value + time value). If you subtract out the value of that option as determined by a blackscholes model the remaining value will be the bond component. Using a RATE function will then give you the implied credit spread.

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Barclays technical introduction to Convertibles is a very good start.

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In classical structural modeling, we have that the firm asset value $A(t)$ is the fundamental stochastic variable, following an SDE like the one presented by @Dom $$\frac{dA}{A} = \mu_A d\,t + \sigma_A d\,W$$ The stock price is then itself an option on the asset value at some horizon $T_H$, $$S_t = S(A(t), \mu_A, \sigma_A, T_H)$$ and the convertible ...

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The parity in this picture is given as the percentage of the face value. The stock price is given in HUF. I checked the stock price, It reached 16600 in september 2013. The EURHUF that time was something like 299, but we should now the exact time this picture was taken. So we have everything to calculate the parity: \$\text{Parity} = \text{Conv Ratio} \cdot ...

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The above gives you the value of the option in the convertible bond. Next step, look at the price of an exchange-traded option to see what the embedded convertible bond option is worth. That can tell you if the convertible bond is over or under priced - compare the market value of the option to the implied price of the option (scaling prices to the same ...

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Here is a new paper written by Tim Xiao at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2400101

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You are mixing terms here. The definition of an "interest rate" is typically a simple interest rate as applies to the Principal of a loan. The unpaid interest rate is not compounded. This is owed at the conclusion of the loan or when converted to debt. Typically rolled into the equity stake. The definition of "discount" is what the convertible debt holder ...

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If there is no chance of default, and you have an extremely simple set of terms and conditions (T&C) on the bond, then the two are equivalent. In the real world T&C are complex for all bonds currently traded, and default is important. Therefore something closer to the binomial model, which allows the embedded option to disappear in the event of ...

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What convertible securities are Convertible securities are typically either bonds or preferred stock that combines typical features of their respective asset class with exposure to price changes in the common shares of the company. Convertible bonds will usually carry an interest rate, par value, and maturity date just like any other bond. Convertible ...

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