# Tag Info

### Transform of payoff function $w_c=(\sqrt{y}-K)^+$

The fourier transform is $$\hat{w}_c= \int_{-\infty}^\infty (\sqrt{y}-K)^+ e^{-i\phi y}dy = \int_{K^2}^\infty (\sqrt{y}-K) e^{-i\phi y}dy$$ Now do a change of variable ...
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### Architecture of a global pricing library with immutable payoffs

That's the best question that nearly no one asks. I'm with you on Quantlib and Strata, haven't really seen a very good design around but I've seen quite a few bad ones. It is definitely doable and has ...

### What does "first-order effect" mean?

Assume you have a consumption $c$ and an asset with the payoff $x$. Cochrane states that if you add "a little bit of this asset" in your portfolio first you care about the correlation between the ...
Accepted

### Replication of the payoff of a chooser option

Consider a European chooser option which allows you to choose at time $\tau$ if you want to receive a put option and call option with maturity $T>\tau$. At time $\tau$, using the put-call parity, ...
• 16k
Accepted

### What does it mean by "A one period bond is a claim to a unit payoff." from Cochrane?

A bond repays its notional face value (plus interest sometimes), not the original purchase price. Do not assume the the price you pay for a bond is its face value. Sometimes a law or a regulation (...
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### What does it mean by "A one period bond is a claim to a unit payoff." from Cochrane?

That simply means that a bond pays one unit of the currency in any state (regardless what happens in the future, i.e. there is no default risk about the payoff of a bond). So you will receive 1 in ...
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### Discontinuous derivative payoff approximation

We should be able to replicate the payoff exactly in each of the two regions $S_{T}\leq k_{1}$ and $S_{T}\geq k_{2}$. From the first, $$a_{0}+a_{1}S_{T}+a_{3}(k_{2}-S_{T}) =S_{T}$$ so, matching ...
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### Explaining an Option product: SIX Discount Certificates

From @noob2's link, it looks like the product behaves like a basket of a long position in the underlying and short an out-of-the-money call option; thus the discount vs the price of the underlying is ...
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### Construct a portfolio of European call options with a certain payoff function

You can check my answer to this question for general details on how to solve this kind of problem. Let $C_X(S_T)$ and $P_Y(S_T)$ be a call and a put option with strikes $X$ and $Y$ respectively, ...
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Accepted

### How do we calculate option payoff before expiration?

Somewhere must be a little error, here I used $r=0.02$ and $\sigma=0.25$. In black you have the payoff and in red the current price of the portfolio. Note that as the time to maturity decreases, the ...
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