The Bond Floor is the fixed income value of the convertible bond taking into account the cash flows (coupons and redemption) and also the bond optionality : bondholder put and hard call.
The Bond Floor is also the value of the convertible bond without its conversion option, which can be seen in the chart when the conversion option has no value for a spot at zero.
Here for a zero coupon plain vanilla convertible it is equal to the present value of the redemption.
Parity
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The Parity is the value of the convertible bond upon conversion into the underlying shares.
It is defined as the conversion ratio times the underlying share price (and usually expressed in the same unit as the price).
Parity = Conv. Ratio × S
Conv. Premium
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The Conversion Premium is the percentage added to the parity to obtain the convertible bond price.
This is the premium paid over the intrinsic value of the underlying shares to obtain a convertible bond.
Conv. Premium = ( Price - Parity ) / Parity
Delta
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The Delta is the change in the convertible bond price for a small change in the share price.
Delta represents the equivalent number of shares that replicates the convertible bond price moves when the share slightly moves.
Delta is therefore the number of shares needed to hedge this dependency with respect to the share price, and is also called Hedge Ratio.
Δ = ∂ P / ∂ S
Here Delta is expressed as the change in the convertible bond price for a one point move in parity.
Gamma
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The Gamma is the change in the Delta for a small change in the share price.
Γ = ∂ Δ / ∂ S = ∂2 P / ∂ S2
Gamma quantifies the convexity, i.e. the number of shares to add to the Delta in order to replicate the convertible bond price moves when the share price increases, or symmetrically the number of shares to deduct to the Delta in order to replicate the convertible bond price moves when the share price drops.
Δ(S+δS) = Δ(S) +Γ δS + ℴ(δS)
Here Gamma is expressed as the change in the Delta for a one point move in parity.
P(S+δS) = P(S) + Δ δS + ½ Γ (δS)2 + ℴ((δS)2)
Vega
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The Vega is the change in the convertible bond price for a small change in the model volatility.
Vega = ∂ P / ∂ σ
Here Vega is expressed as the change in the convertible bond price for a one point change in the volatility.
Theta
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The Theta is the rate of change in the convertible bond price with respect to the time.
Theta = ∂ P / ∂ t
Here Theta is expressed as the equivalent annual move of the convertible bond price, to be comparable to the annual rates.
Rho
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The Rho is the change in the convertible bond price for a small change in the yield curve.
ρ = ∂ P / ∂ r
Here rho is expressed as the convertible bond price change for a 100bp shift in the yield curve.
Sensitivity
Equity Sensi.
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%
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The Equity Sensitivity is the percentage change in the convertible bond price for a small percentage change in the share price.
The Equity Sensivity is also called Delta Outright, because it represents the change in percentage of the convertible bond market value due to a change in percentage of the share price. The Equity Sensivity is the equivalent of Elasticity for equity options.
Equity Sensivity = Δ × Conv. Ratio × S / P
Equity Sensivity = Δ / (1 + Conv. Prem.)
Gamma 1%
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%
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The Gamma 1% is the gamma expressed for a one percent change in the share price.
Gamma 1% is the change in the Delta for a one percent change in the share price.
Convexity 20%
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%
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Convexity 20% represents the percentage change in the convertible bond price due to convexity for a 20% change in the share price.
This is the percentage to add to the performance due to the equity sensitivity to obtain the convertible bond price
It is obtained with the gamma.
Px Chg (S +20%)
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%
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Px Chg (S +20%) is the percentage change in the convertible bond price for a 20% change in the share price.
This is a repricing, or stress-test, for the specific share price taking into account the whole profile of the convertible bond and not only delta and gamma.
Px Chg (S -20%)
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%
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Px Chg (S -20%) is the percentage change in the convertible bond price for a -20% change in the share price.
This is a repricing, or stress-test, for the specific share price taking into account the whole profile of the convertible bond and not only delta and gamma.
Vega %
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%
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Vega % is the Vega expressed as percentage of the convertible bond price
Theta %
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%
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Theta % is the Theta expressed as percentage of the convertible bond price
Rho %
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%
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Rho % is the Rho expressed as percentage of the convertible bond price
Px Chg (Credit +25%)
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%
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Px Chg (Credit +25%) is the percentage change in the convertible bond price for a 25% proportional shift of the credit spread.
Controls
Rho = f(S)
Vega = f(S)
Theta = f(S)
What you can do:
Increase or decrease the model inputs with the +/- buttons
Write the model inputs and valid with enter to compute
Highlight the tangent to the price by passing the mouse over the green circles
Compute all model outputs by passing the mouse over a circle
Click on the circle to show or hide the tangent
Show the definitions by passing the mouse over "?"
Show specific legend by passing the mouse over the lines