# Questions tagged [put]

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### How to Take Advantage of Arbitrage Opportunity of Two Options

I got the following interview question and corresponding solution, but I have a different understand that might be wrong, so I really appreciate your advice on it: A European put option on a non-...
14 views

### What is the payoff matrix of a set of put option that completes the market?

For example, there are three states of nature but only one security yielding payoffs {1,2,3} in the three states. What would be the set of put options that completes the market? I know that if it his ...
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### How can the solution to a optimal stopping problem be superharmonic?

A general result (Peskir and Shiryaev: Optimal Stopping and Free Boundary Problems, 2006, Thm. 2.4, Page 37) is that the solution to an optimal stopping problem $\sup_\tau EG(X_\tau)$ where $X$ is ...
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### some questions about pricing an asset or nothing put option with a strike price equal to St

I am working on a homework exercise where the aim is to price an asset or nothing put with K = St, offcourse the normal formula could be used St * N(-d1), but I was wondering if pricing the asset by ...
89 views

### Is the european put option an increasing function?

My question is to show that the function $K \rightarrow p(T,K)$ is increasing. T being maturity time,K being any strike and $p(T,K)$ is a european put option. My only approach to this question has ...
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### HEDGING WITH A PUT OPTION

In the following example, for 3rd question and 4th question why do we have to add (Stock price in three months - Current stock price) to put option profit? Thank you in advance.
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### Kingdom of Denmark Nikkei put warrants

I have read in a book from Emanuel Derman that Goldman Sachs manufactured a derivative in the early 90's that consisted of buying cheap puts on th Nikkei index (and paid in Yen), combined them which a ...
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### Pricing of European put option with binomial model

This is an exercise from Mark Joshi's book (exercise 3.6): A stock is worth 100. Each month its value increases or decreases by precisely 10. The riskless bond is worth $e^{rt}$ at time t years with ...
197 views

### Can increase in volatility reduce the price of a deeply in-the-money European put?

Hull states that option prices increase with an increase in volatility. I think that statement could be false in a specific scenario: when we are considering a deeply in-the-money European put ...
61 views

### Prove the following Call and Put relationship: [duplicate]

I need to prove that $$c(S,X,T)=\frac{X}{F}p(S,\frac{F^2}{X},T)$$ where $$F=Se^{(r-q)(T-t)}$$ I am having trouble proving this relationship. Is this relationship even possible? If so, can someone ...
58 views

### Computing option price with rates only

Hi I am learning about options and came across this example: The spot FX rate AUD/USD is 0.6868, the 6 month ATM implied volatility for AUD/USD is 7.7% p.a., for the 6 month USD deposit rate is 2.28% ...
103 views

### What are the main problems for calculating the implied volatility of in the money American put options?

As stated in the question I have a problem with calculating the implied volatility for in the money put options I have a data set of 2.6 million American style plain-vanilla call and put options. For ...
180 views

### American put option. Exercise time is a random variable, calculation of expected payoff

I got an American put option, where the payoff is $V_\tau = \max(K - X_{\tau}, 0)$ and $X_{\tau}$ is the price of an underlying at the stopping time $\tau < T$. The underlying follows a standard ...
84 views

### Feynman-Kac to derive stochastic representation

$u_t + \frac{1}{2}\sigma^2x^2u_{xx} - \alpha + \lambda((K_d - x)^+ - u) = 0$ with terminal condition $u(T, X) = (K_m - X(T))^+$ $dX = \sigma X(t)dW_t$ $\alpha$ and $\lambda$ are constants Ok so ...
655 views

### Delta Hedging/ Exchange for Currency Options

I'm looking at 2 cases of hedging EURUSD, using call spread or range forward. Lets say spot is 1.1300 and my buy call is at 1.1300 and sell call is at 1.1500. Hypothetically I'm assuming that this is ...
62 views

### is relating bounds to relation between time to maturity and european put option price correct?

J.C. Hull derives the following relation $$Ke^{-rT} - S \le p \le Ke^{-rT}$$ where $p$ is european put option price, $K$ is strike price, $S$ is stock spot price,$r$ rate of interest and $T$ ...
41 views

### Return on Investment for rolled options position on margin [duplicate]

I'm trying to calculate my return on investment (ROI) for an options position on margin that has been rolled. I'll give an example: Sell to Open (STO) a naked put position, for which I collect 100 ...
2k views

### Positive theta on a long put?

I am trying to hand-price options under the Black-Scholes model. Given the following parameters: Stock price: $12.53$ Strike price: $14.00$ Risk-free rate: $0.03$ Annualized Volatility: $0.10$ Time ...
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3k views

### Pricing American Put Options via Binomial Tree in Matlab

I currently am completing a Computational Finance Assignment, and am trying to figure out how to alter this Matlab code which prices a European put or call option, in order to price an American Put ...
281 views

### Finding the replicating portfolio a European T-claim (put)

I have $$dX_0(t) = ρX_0(t)dt ; \qquad X_0(0) = 1\\ dX_1(t) = αX_1(t)dt + βX_1(t)dB(t) ; \qquad X_1(0) = x_1 > 0$$ as the classical Black-Scholes market. I a trying to look for the replicating ...
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### Understanding the relationship between the Black-Scholes formula and a replicating portfolio

I'm self-studying and I'm considering the below example. The specific example is not especially relevant, but I included it for reference. I'm trying to understand the relationship between a ...
370 views

Suppose a put option on a stock $S(t)$ following a Geometric Brownian motion is given, with strike $K$ and maturity $T$. Let us denote its price at time $t$ by $p(t,S(t))$. Now, by no-arbitrage ...
764 views

### How to create a synthetic put?

I have been reading into Hull's section on portfolio insurance through synthetic puts. My understanding is that in order to replicate a put we should replicate it's delta. Proceeding, Hull states ...
112 views

### Put Volatility Smiles and Implied Volatility

I have been observing the option chains of put options with differing maturities. I have noticed that those puts with a close expiry date have the steepest volatility smiles. Can someone please ...
110 views

### Put call parity: when are the premiums the same?

Please explain why put call parity could be compared to the payoff of a long forward contract. ie. $C_E-P_E=V_X(0)$ where $C_E,P_E$ are the call/put premiums and $V_X(0)$ is the value of a long ...
3k views

### Use of cash delta vs forward delta and the mirror image rule

There has been no mention in this text of why this formula uses forward delta not cash delta. Why should have this been obvious to the reader? How can a put be delta neutral at 30%, what does this ...
59 views

### Enron - RhythmsNet hedge

I am reading "Power Failure: The Inside Story of The Collapse of Enron" By Mimi Swartz, Sherron Watkins. In the book, the following transaction is described: Enron had USD200mn worth of futures on ...
291 views

### Payoff of a butterfly c++

I would like to price options (call, put,, butterfly) with monte-carlo method, but actually I need the expression of the butterflay payoff; Could you ^please help me !
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### Volatility Skew for Put and Call options [closed]

Given that the implied volatility follows volatility skew, which one has higher implied volatility? At-the-money put 40 (spot = strike = 40) or at-the-money call 160 (spot = strike = 160)? I am not ...
114 views

### American put option and rising interest rate

Will a rise in interest rate always result in a lower price of an American put option?
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### American put on a foreign currency

I know that For an American-style put option, early exercise is a optimal for deep in-the-money options. In this case, it may make sense to exercise the option early in order to obtain the profit ...
### How do I prove that $\lim_{K\searrow0}\frac{P(K,T)}{K} = \mathbb P(S_T=0)$?
I am trying to prove that $$\lim_{K\searrow0}\frac{P(K,T)}{K} = \mathbb P(S_T=0)$$ where $P(K,T)$ denotes the put option price with maturity $T$ and strike $K$ for some stock $S$. Assuming interest ...