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Questions tagged [derivatives]

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

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1k views

What is the difference between funded and unfunded derivative?

What is the difference between funded and unfunded derivative? Can anyone explain the difference between these two?
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1answer
180 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
287 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
167 views

Binary option analytical formula

Given $r=0$, $\sigma(K)=\text{const}$ and: $$ \text{Binary} = \lim_{ε → 0} \frac{(C(K,\sigma (K))-C(K+ε,\sigma(K+ε)))}{ε} $$ I have to find the analytical expression for the above. Since $σ(K)=\...
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296 views

The dice game and derivatives trading

I happened to a interview question: Give a equal dice, you will gain the money which is the number you roll, then how much will you pay for the game. Naturely, the answer is 3.5. But the interview ...
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1answer
183 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
92 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
230 views

at-the-money short term straddle and the implied vol

Here is a passage from "Advanced Equity Derivatives: Volatility and Correlation" by Sebastien Bossu, Wiley (2014). We see the prox $\beta_0,$ it seems to use the approximation that ...
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2answers
202 views

Pricing 0% interest rate Floor Black Model

I'm having some trouble pricing a 0% interest rate Floor following Black's formula. The term d1 contains the expresion Ln(Forward/Strike) if the strike is exactly 0 this expresion yields an ...
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1answer
157 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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239 views

Refer some most recent books of derivatives pricing by C++

Could you refer some most recent books of derivatives pricing by C++ including Tree method, Finite difference method, Monte Carlo etc. Once I read a series of <...
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0answers
77 views

Pricing of Swaption by Proxy and Monte Carlo

here's the problem. Suppose you want to compute the price of a Call option on a Swap contract. Let $T$ and $T+S$ the times (in year fraction) where the Swap lives and suppose that the fluxes of the ...
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1answer
269 views

Log-moneyness definition [closed]

Define the time-0 log-moneyness of a call on stock $S$ with strike $K$ and expiry $T$ to be: $$\log(S(0)\exp(rT)/K)$$ What does it mean for the strikes K to be at-the-log-moneyness?? I guessed this ...
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1answer
81 views

IVF and implied distribution of underlying in John Hull's book

There is a statement in John Hull's book Options, Futures and Other Derivatives 9th page 633 for the relation between ...
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1answer
55 views

Cash as Collateral in OTC Market

In OTC market Collateral Posting as cash is normal, so when it is said Collateral Posted as USD CASH Does that mean Actual amount of currency is posted electronically (or any security is posted) ...
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1answer
132 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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2answers
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Cash-settled swaptions

I was wondering, what is the motivation behind the payoff of the cash swaptions being multiplied by the swap annuity? $$c(S_{\theta, T})=\sum_{i=\theta+1}^{T}\tau_i\frac{1}{{(1+S_{\theta,T}(\theta))}^...
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1answer
342 views

Differences between Snowball, KIKO and TRF derivatives?

Can you explain what are some similarities and differences between snowball, KIKO (knock in knock out) and TRF (target redemption forward) derivatives?
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1answer
113 views

Replicating a square derivative with calls and puts

I have a derivative that pays off $S_T^2$ at time $T > 0$ with $S_T$ denoting the price of a non dividend-paying stock at $T$. I came across a question about how one can statically replicate this ...
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1answer
273 views

quanto adjustments

Here is quanto adjustments in John Hull's book Options, Futures and Other Derivatives 9th ...
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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
88 views

Zero value of cash flow for future in Shreve's book

Here is the statements of future price in Shreve's book Stochastic Calculus for Finance II page 244 to proof the ...
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1answer
279 views

Build a Synthetic Loan for Personal Finance

Suppose I am short of cash and want a loan for some mundane objective like travelling or buying a car. The interest rate for personal loan with my bank is too high. Is there any way in finance that ...
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1answer
99 views

How to understand closing position of futures

When we want to close out the position of futures prior to the delivery period, you will entering into the opposite trade to the original one. Equivalently, except ...
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1answer
801 views

What exactly is a deposit futures contract?

I have been working with Deposit Futures and the Brazilian One-Day Interbank Deposit Future but I can't get my head around them. What exactly is delivered and when? What is the contract a right to?
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1answer
132 views

How do I modify my basic black scholes model in Excel to price american options?

I've modeled a basic black scholes model in Excel and I have been using it to price European options for backtesting purposes. This has been working fantastically and I would like to adjust this to ...
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0answers
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The interpretation of discounted Greeks

I understand that Delta measures the rate of change of the theoretical option value with respect to the change of the underlying asset price. This also represents the number of shares a call option ...
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0answers
59 views

How do I build an EQ Options backtesting system?

I have a current problem on hand. I've been building my backtests in excel, using basic logic formulas and loading huge historical data sets going back from 1990s. Although this has been rather ...
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1answer
57 views

CDS for Funding

I was wondering if anyone is familiar with how credit default swaps can be used for corp funding and financing. I came across an old case where a bank created a funding structure for a client (asset ...
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1answer
80 views

Is there a way of synthetically deleveraging a Real Estate portfolio?

If I manage a Real Estate portfolio with approximately 400 million in debt, which is roughly 50% Loan-to-Value (the properties are worth about 800 million). Is it possible to synthesize a bond ...
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1answer
103 views

Reference for why a derivative is a derivative and not say an insurance contract

I recently spoke to an options trader that tried to demonstrate option pricing by considering a random walk of balls dropping down a lattice so the underlying stochastic process is a simple random ...
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2answers
2k views

Why discounted derivative price is a martingale?

Usually after showing that discounted stock price process is martingale under the risk-neutral measure, most authors say that this implies that the discounted derivative price process is a martingale ...
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0answers
100 views

Adjusting implied vol for skew

I'm trying to evaluate fair volatility, but I am stuck on how to adjust the implied volatility for skew. When historic implied vol is calculated, obviously the strike used changes as the underlying ...
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1answer
209 views

Pricing the Passport option

Suppose underlying asset $S$ $$dS = \mu Sdt + \sigma Sd W$$ our portfolio $\pi$ consist with $q(t)$ stock $S$ and cash $\pi - qS$...
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2answers
865 views

Delta Hedging with fixed Implied Volatility to get rid of vega?

I'm wondering if i should use a floating IV or a fixed IV to delta hedge my options every day. I've read this post but would like different information : Delta Hedging with fixed Implied Volatility ...
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58 views

Solving for roots of a stochastic pay-off function

I have a pay-off function for a derivative which is defined by the Heaviside difference between $G$ and $B$ shifted by $-F$. To find the value of $V_{t=0}$, I need to find $\tau$ when $\frac{dV}{dt} = ...
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3answers
163 views

Why don't we take the differential to the Delta in the Delta hedge-portfolio

For option $V(S,t)$ with underlying asset $S$, we have a hedge portfolio $$\Pi = V(S,t) - \Delta(S,t)S$$ I always confuse here, when we take the differential of $\Pi$ $$d\Pi = dV -\Delta dS$$ why ...
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1answer
160 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
86 views

Cap option on Libor

We denote discount factor $D(t),$ zero coupon bond $B(t,T),$ $E_t[X] = E[X|\mathcal{F}(t)]$ and $T$-forward measure $E_t^{T}[\ ]....
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1answer
262 views

Replicating a portfolio with a certain payoff function

Assume there are two stocks $S_1$ with price $p_1(t)$ and $S_2$ with price $p_2(t)$ where $t$ indicates time. Assume, there is a hypothetical derivative $D$, which is such that, price of $D$ at a time ...
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1answer
511 views

Why does a futures price converge to a spot price?

I've sort of get the arbitrage logic of it, i.e if the futures price is more expensive than spot price, then investors would short the contract and buy the asset for delivery. Correct me if i'm wrong. ...
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56 views

Value of American option after exercise

Suppose $V^+(S,t;K)$ is the value of a American option with strike $K$ before the exercise, and $V^-(S,t;K)$ is the value after exercise. Then how to understand the inequality $$V^+(S,t;K)\geq V^-(S,t;...
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1answer
505 views

Black-Scholes formula for Poisson jumps

For underlying asset $$d S = r S dt + \sigma S d W + (J-1)Sd N$$ here $W$ is a Brownian motion, $N(t)$ is Poisson process with intensity $\lambda.$ Suppose $J$ is log-normal with standard deviation $\...
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1answer
237 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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1answer
338 views

Delta Hedging: Clarification example of the book “Hull, Options, Futures, and Other Derivatives” [closed]

By "Hull, Options, Futures, and Other Derivatives": Suppose that, in figure,the stock price is \$100 and the option price is \$10. Imagine an investor who has sold 20 call option ...
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1answer
105 views

What is the best trading simulation platform for futures, swaps, options, etc.?

I've just started studying derivatives from the "Options, futures, and other derivatives - J.C. Hull" and I'd like to see how to do hedging and trading transactions through a simulation platform or a ...
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1answer
46 views

Factors that make sell-side valuations of equity derivatives differ

If I ask a sell-side desk "A" for a "valuation" of a relatively simple OTC product (equity derivative, or 1st generation equity exotic), what are the reasons/main reason why a different sell-side desk ...
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1answer
1k views

How to understand the market price of risk

Consider the stochastic vol: $$dS = \mu Sdt + \sigma SdW_1$$ $$d\sigma = p(\sigma,S,t)dt + q(\sigma,S,t)dW_2$$ $$dW_1dW_2 = \rho dt$$ We want to obtain the price of option $V(\sigma,S,t),$ we use the ...
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0answers
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Boundary condition of lookback option

This is a well know conclusion of the boundary condition of lookback option. Here $$\dfrac{d S_t}{S_t} = (\mu - D)dt + \sigma ...
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2answers
126 views

Why is option value different from discounted CF [closed]

as stated: why other assets' value can be determined by taking into consideration their expected cash flow (CF)? I read an argument which refers to arbitrage, but I wonder is there an additional ...