Questions tagged [derivatives]

A financial contract whose payoff is linked to the evolution of an underlying security.

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61 views

Delta Hedging Example

I was reading Dynamic Hedging by N. Taleb and in the chapter dedicated to the delta, there is this example of a trader position in options (one-month European call, flat yield curve, forward is ...
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62 views

What model do market makers in equity derivatives commonly use to price, hedge, and fit the IV surface?

What is the industry standard/common model used by market makers in equity derivatives to trade across the IV surface?
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34 views

Difference in utility of cap/floor and FRA

What is the difference in utility for cap/floor and FRA? To me their function looks very similar. Are they used for different objectives. One thing I know in difference is that the pay off for cap is ...
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61 views

Banks' use of written interest rate options

I study US commercial banks data. I look at the notional amounts of their different OTC interest rate derivatives for the recent years. When I look at non-dealer banks (i.e. end-users), I find that ...
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73 views

Bates Model Jump Percentage Parameters

I am trying to calculate the jump parameters for the Bates volatility jumps, specifically, the mean of the jump percentages, $\mu_j$. For the value of $J$, I am using jumps $|\frac{s_{i}-s_{i-1}}{s_{i-...
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77 views

How to determine expected returns of an options portfolio?

Lets say I have a delta neutral portfolio, iron condors on spy for example. I'm short a call credit spread and a put credit credit spread of equal widths. I would like to determine the expected ...
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625 views

Cash-or-nothing and Asset-or-nothing price derivation

I was wondering how to derive the price of a cash-or-nothing and asset-or-nothing option by trying to work out the expectation under the risk-neutral measure, while assuming that the underlying ...
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156 views

Exotic derivatives - Replication

I would like to replicate the payoff Max(0, Min(S1, K) - S2) with a combination of the following derivatives: -> option on S1, strike of our choice -> option on (S1-S2), strike of our choice -> A ...
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635 views

Multi-currency CSA discounting curve construction

I have a number of eur/usd and gbp/usd MtM Basis swaps that are collaterized in USD. For the non-usd legs I'm constructing the muti-ccy csa discounting curve. Im using forwards for the short end of ...
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1answer
288 views

Exercise Probabilities Vanilla Cap/Foor

When looking at the discounted pay-off formulas of a vanilla caplet and a vanilla floorlet $\frac{\Delta\tau}{1+r_k\Delta\tau}\max(r_k-r_{cap},0)$ $\frac{\Delta\tau}{1+r_k\Delta\tau}\max(r_{floor}-...
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178 views

Derivative and Credit Risk Modelling

I am looking at acquiring a system to help with multi-instrument modelling. Across the spectrum Equity/FI/Swap/Repo/CDS/FxSwap/Forward/Future/etc for vanilla and more complex derivatives. The modeling ...
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64 views

Literature to Learn about Different Instruments

What is a good source of literature to learn about the specifics of various instruments that are traded? For example, suppose I wanted to know more about MBS's, i.e. how exactly they are securitized, ...
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1answer
493 views

decompose correlation swap pnl

For a Variance swap we can split the pnl into a realized part and a "forward going" part. To be more precise: Assume we enter the trade at t0, and the variance swap has tenor T and a strike $Kvar$. ...
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87 views

why many option contract price less than minimum boundary price?

I downloaded data from NSE(National Stock Exchange) website regarding closing price of European Call Option written on Index. From standard textbook, I read that option contract must satisfy $C(t) \...
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1answer
271 views

What is the filtration described?

What is the filtration $(\mathfrak{F}_t)$ encircled below? Is it $(\mathfrak{F}_t) = (\sigma(W_t)) = (\sigma(\tilde{W_t})), t \in [0,T]$? Or is it $(\mathfrak{F}_t) = (\sigma(\hat{W_t})), t \in [0,T]...
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315 views

Weighted average implied optionlet/swaptions volatility

Let an implied volatility curve/surface is made up by optionlets or swaptions Black's implied volatility. If you wanted to price, say, a FRN with cap and/or floor, a CMS et cetera you would input the ...
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86 views

FRA-Strategy: Make 3-month and 1-year Excess returns comparable

I am trying to analyze an investment strategy that tries to exploit the empirical difference between forward interest rates and realized spot rates. I am using FRAs to capture the difference. I am ...
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101 views

What models for backing out Equity IVOL [duplicate]

Possible Duplicate: How should I calculate the implied volatility of an American option in a real-time production environment? I am starting a project and would be grateful for some practical ...
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3answers
846 views

Commodity Asian Swaps

I'm trying to find info about asian swaps on oil/energy products and about their pricing methods. However, all I could find are on asian options. Would be glad if you can provide me with some ...
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2answers
4k views

Long/Short Vega and Option Positions

Why do you get long vega when you buy an option and short vega when you sell an option? I would have thought that for both buying and selling options the vega would change according to whether the ...
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3answers
242 views

What is the name of this product?

Consider the payoff =$S_T1_{S_T>K}$ where $S_T$ is the asset price at maturity. What is this type derivative called? and is it a liquid option?
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1answer
48 views

Call price in case of AOA

I have this exercice, and for the last question, i tried to say that with lower bound, $C > S_0 - Ke^{-rT}$ which is $-8$ something but it doesn't make sense so i don't know what to do. Could we ...
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2answers
168 views

Valuation of Total return swaps (TRS)

I have seen a TRS being valued which has an index as underlying on the asset side. It also has a coupon rate associated with it. Asset leg is calculated by taking ...
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2answers
169 views

Volatility smile shows individual Put and Call IV or combination

IV is calculated per strike AND option type basis(for example WTI 50 CALL its x and WTI 50 PUT its y). The question is when its shown in "Smile" its just shown on strike basis, so does that mean lower ...
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1answer
237 views

Lattice pricing of derivatives under multi curve framework (OIS and LIBOR)

My goal is to price various derivatives resetting to 1M and 3M LIBOR via using a lattice. I have calculated an OIS curve for discounting and adjusted 1M and 3M LIBOR forward curves to be consistent ...
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1answer
808 views

Use of cap volatilities

I have a cap volatility surface for the 6 months Libor. Can I use the same cap volatility for every cap's caplet to valuate the full cap? Example: Valuate a 18M cap (Libor 6M) by valuating 3 6M ...
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1answer
309 views

Number of Time Steps in Binomial Option Pricing - Problem?

I am trying to price a digital option and the final price under different number of time steps are as follows: Is it possible to have a graph like this?
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1answer
326 views

How to use reflection principle to solve the analytic solution of double barrier-out-call

We consider up/down-out-call whose payment $$V(T,S_T) = \Psi(S_T)\mathbb{II}(S_T),\ V(t,B) = 0.$$ Here the range constraint function is ...
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1answer
563 views

What are the differences between CFD and SSF?

What are the intricate differences between SSF and CFD? The similarities are that both take into account interest and settled daily thus looks more or less the same pima facie.
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1answer
51 views

partial derivatives of multivariable function

Looking to verify whether the following formulation is correct. Suppose we have the following function, relationships: $$y=f(x)$$ $$x=g(a,b)$$ $$y=f[g(a,b)]$$ Is the below correct (including ...
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1answer
112 views

Any good book recommendations for learning The Greeks?

I am interested in getting a good "feel" or intuition for the BSM Greeks. Specifically, i'm looking for a book which is light on the math (but not too light) and easy to read and understand. I am also ...
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1answer
101 views

Static hedge forward swap using zero coupon swaps

I'm trying to create a static hedge for a forward swap using two spot starting zero coupon swaps (to prove that there is no convexity adjustment needed). Here are the instruments - Paying fixed in ...
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1answer
182 views

Rebasing of Cap Volatilities

I recently found this article where towards the end the author describes a method to rebase cap volatilities. Their method works like this: for a fixed strike assume that you are given the implied ...
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1answer
424 views

Pricing of a derivative using Risk Neutral Valuation.

I am new to option pricing and following problem came up that I don't understand how to handle. A derivative will pay out dollar amount equal to $$\frac1T\ln \frac{S_T}{S_0}$$ at maturity, where $...
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1answer
456 views

Quantlib: Getting error trying to price a Swap

I have bootstrapped my curve based on end-of-day data for 24th Nov, 2017 I am then using that to price a off-market swap as below: ...
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1answer
455 views

Books about Monte Carlo Simulation on derivatives with Python

I am looking for a good reference for Monte Carlo simulation applied to derivatives with Python. Most books I found until now deal with C++... I have found "Derivatives Analytics with Python" by Yves ...
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1answer
106 views

Calculating expected loss using actual probabilities

I'm calculating expected loss on fixed-income using actual default probabilities and risk-free rate as the discount factor. I understand this is not theoretically correct. In absence of risk-neutral ...
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1answer
196 views

eurodollar future

I just found out about eurdollar futures and I am confused. A eurodollar future contract is defined as a cash settled future based on a Eurodollar Time Deposit having a principal value of USD $1,000,...
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1answer
159 views

What are good risk management books or docs? [duplicate]

I have an unusual request/question. I was wondering if anyone here could recommend me some books about risk management and equity derivatives. I am about to do an internship as a risk analyst on an ...
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1answer
2k views

What is CVA (credit valuation adjustment)?

According to Wikipedia, CVA is defined as the difference between the risk-free portfolio value and the true portfolio value that takes into account the possibility of a counterparty’s default. What ...
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1answer
82 views

Is it possible to approach finding the risk premium of this derivative using Ito's Lemma?

I understand the author's intended solution to the below problem, but I thought I would see if I could solve this using first principles and Ito's Lemma instead for practice. Let $V(S(t), t) = e^{rt}\...
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2answers
529 views

Prove that the vertical spread condition is bounded

I need to prove that vertical spread is bounded, by using no arbitrage condition. 0 > (C(T,K1 )- C(T,K2))/(K1- K2 ) >-e^(-r*T ) I have documented my ...
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1answer
124 views

Beginner question about basis risk

new to the area, and had a question about basis risk. If I entered into a receive fixed pay 1mo Libor swap, why is it good for me if the 1x3 month Libor widens and bad for me when it tightens. Also ...
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2answers
157 views

Is a linear hedge sufficient for most purposes?

I was in a lecture of Bruno Dupire's when he said something along the lines of a linear hedge being sufficient for most purposes. He gave a counter example as well: a corporation producing something ...
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1answer
709 views

Derivative: Delta of a Down and Out Call Option with Barrier=Debt(K)

I am trying to compute the derivative of this function with respect to V0: This is the price of a down and out call option, assuming the barrier equal to the level of debt K. In other terms, I need ...
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2answers
175 views

Analysis of exercising a call option early

Most options traders sell their call options early instead of exercising them, as you would make a bigger profit this way due to being able to salvage some remaining extrinsic value. For example: ...
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1answer
759 views

Why we consider second derivative w.rt price but only first derivative w.r.t time and volatility

What is the reason (better if it is intuitive, and not too math heavy), that when we talk of Greeks, we consider second derivative with respect to price (gamma), but only first derivative with respect ...
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1answer
272 views

Gamma derivation from the expectation

I am trying to derive Gamma from the expectation principle (differentiating under expectation sign). I understand these steps $\frac{d^2 C}{d x^2} = e^{-r\tau} \mathbb{E} [ \frac{\partial}{\partial x}...
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1answer
246 views

Jump-Diffusion Processes

This last quarter of college for senior project, I will be doing research on the application of jump-diffusion processes to pricing derivatives. I was wondering if anyone could recommend any resources ...
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1answer
79 views

Black Sholes option pricing with all but Delta [closed]

I'm trying to setup a little option pricing model in excel. I have all the information for the inputs (interest rate, IVs for different deltas, time to expiry, strike price, underlying price) but what ...