Questions tagged [derivatives]

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

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2
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2answers
256 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
311 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
199 views

How to price up-out-call by solving heat equation like down-out-call

We know that by changing the variables we can obtain the Black-Scholes formula of vanilla call through solving the ...
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2answers
333 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
222 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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1answer
261 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
354 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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1answer
184 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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2answers
843 views

Pricing Cancelable swap

Consider a first hypothetical, a swap. Party 1 is paying 6 month Libor, semi-annually. Party 2. pays $1+3*(\frac{Index_\color{red}{T}}{Index_0}-1) $ only at maturity. Say the notional is 1. $Index_t$ ...
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280 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
119 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
389 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
113 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
72 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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2answers
237 views

How to make the arbitrage if intrinsic value is greater than European call value

It always says if the intrinsic value is greater than European call value, there will be a arbitrage opportunity,but how to construct the portfolio $(S_t - K)^+$ or how to make this arbitrage. By the ...
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1answer
152 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
170 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
378 views

quanto adjustments

Here is quanto adjustments in John Hull's book Options, Futures and Other Derivatives 9th ...
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1answer
131 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
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
1k views

How to measure contango?

Is there any unit of measure for the magnitude of the contango (or backwardation) for futures, so you can compare the contango of many symbols.
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1answer
116 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 ...
2
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1answer
194 views

Physical Measure in Weather Derivatives — Hull

In Hull's 8ed., he states in Chapter 33, Energy and Commodity Derivatives, The second part of the chapter considers weather and insurance derivatives. A distinctive feature of these derivatives ...
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1answer
1k 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
285 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
160 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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61 views

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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1answer
126 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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1answer
65 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
85 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
270 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
1k 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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60 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
175 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
256 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
102 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
608 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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1answer
60 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
682 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
429 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
113 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
49 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
2k 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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48 views

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
143 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 ...
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1answer
245 views

Increasing the correlation of two asset reduce the value of spread option.

We know the payment function of Spread option is $$\max\{X_T - Y_T-K,0\}$$ here $$d X_t = (\mu_x - D_x)X_t dt + \sigma_xX_td W^x_t$$ $$d Y_t = (\mu_y - D_y)Y_t dt + \sigma_yY_td W^y_t$$ $$d W^x_td W^...
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36 views

Floor option EVE risk: Sum of key rate shocks risks vs. the rates parallel shock risk

Consider a model measuring the EVE risk (change in the economic value by shocking the rates; PV01) of a portfolio of vanilla interest rate floor options. Is there any reason for the EVE risk of a ...
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1answer
149 views

When a particular bond is delivered, why there is the need to define a conversion factor? What is its utility?

Where, the conversion factor for a bond (by John C. Hull) is set equal to the quoted price the bond would have per dollar of principal on the first day of the delivery month on the assumption that the ...
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2answers
254 views

What are the books in which to study the basics of the derivative financial instruments?

Books similar to Options, Futures, and Other Derivatives by John C. Hull. I need another academic book that explains the basics of quantitative finance derivatives (forward, futures, options)
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2answers
190 views

The PDE of caplet and floors

I know following PDE is the continuous payment case, but a caplet pays as rate: $\max(r - r^*,0),$ use the hedge portfolio $\Pi = V- \Delta Z$ $$d\Pi = dV- \...