Questions tagged [put]

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1answer
85 views

Can an In-the-Money Put Option's price $>$ its Strike Price?

The screenshot below suggests thatan ITM put option's price can't overstep its strike price? Why or why not?
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1answer
83 views

Why does black scholes model give lower prices for puts with further time to expiry?

Consider BS-model with parameters: Stock = 100, Strike = 100, Texp = 1 year, Vol = 13%, Rf Rate = 3%. For these parameters the BS put price is 3.76. Then consider the same parameters but with Texp = ...
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1answer
48 views

Option trading strategy to test crash risk premium

I would like test if there are "crash risk premia" priced into out-of-the-money puts. My initial thought was to create a portfolio with a short positions in (deep) OTM put options and a long ...
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0answers
33 views

VaR of protfolio with put and call

I've stumbbled into this question in a job interview and didn't know how to answer it: Calculate the VaR of a portfolio where you are long put and long a call
1
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1answer
74 views

Arbitrage strategy using binomial tree

Suppose that we have a one step binomial tree model for a company. Lets say that the time per step is T, and that price of the stock can go up to $p_1$ or go down to $p_2$. Suppose a T-month European ...
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0answers
18 views

Static hedge for Down-and-out put option

I am trying to compute the static hedge for a down-and-out put option with the barrier above the strike using the put-call symmetry. I am okay with the example in the note with the call option but I ...
1
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1answer
65 views

Most profitable PUT strike price in these times of high volatility?

At close 3/13/20 SPY was at 270.2, by close 3/16 it dropped to 239.41 ~ 8.8% drop... I'm looking at how to capitalize on these big swings with options. I'm backtesting option strategies and plotted ...
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1answer
39 views

Is this the present value of a short position on an option?

Consider a European put option, whose price at time $0$ is $\Pi_0$. Set: $$\mathcal{L}_0=\Pi_0 - P(0,t_M)\Pi_{t_M}$$ where 0 < $t_M$ and $P(0, t_M)$ is the discount factor from time $0$ to time $...
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0answers
17 views

Synthetically sell to close puts in limited-margin IRA

Suppose: I bought an American put on a stock in a retail brokerage IRA, where I can't sell short or write uncovered options. The put is ITM and has served its purpose for hedging. The put is thinly ...
1
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1answer
82 views

Valuation Down-And-Out Put Option via Rubinstein Closed-Form Solution

I am trying to understand the closed form solution for evaluating a down-and-out put option of Rubinstein and Reiner (1991) as stated in Baule and Tallau (2011) for the valuation of bonus certificates....
2
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1answer
335 views

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-...
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0answers
16 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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0answers
52 views

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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1answer
49 views

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 ...
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1answer
99 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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1answer
52 views

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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0answers
108 views

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 ...
3
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2answers
94 views

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 ...
5
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4answers
293 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 ...
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0answers
66 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 ...
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1answer
64 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% ...
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0answers
241 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 ...
6
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3answers
272 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 ...
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0answers
97 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 ...
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1answer
1k 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 ...
2
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1answer
78 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 $T$ ...
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1answer
42 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 ...
3
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1answer
4k 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 ...
2
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1answer
141 views

Perpetual Put vs European Put

I am looking at a perpetual put option where the strike price is initially the stock price $K(0)=S(0)$ (i.e. at the money), but the strike price grows at the constant risk-free rate $r$ [i.e. $K(t)=S(...
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1answer
539 views

Pricing perpetual American put option when interest rate is equal to 0

Let us consider perpetual American put option with interest rate: $r = 0$. The Black-Scholes equation in this case has the form: $$ \frac{1}{2} \sigma^2 S^2 \frac{d^2 V(t, S)}{dS^2} + (r-d)S \frac{dV(...
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0answers
70 views

Different versions of Put-Call Parity

Why is it stated sometimes that $C - P = F$ and in wikipedia it statest that $C - P = D(F-K)$, where D is the discount factor and K is the strike (of both the call and put?). Is this just affected ...
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0answers
155 views

Perpetual American put option with zero interest rate

I want to find an optimal time when we should exercise perpetual American put option. In other words I want to maximize the following equation: $$ V(S) = \sup_{\tau \in \mathcal{\tau}}\mathbb{E}[e^{-...
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1answer
867 views

When does the CBOE Put Protection Index (PPUT) make profit?

In my question, as stated in the title, I aim to understand when the strategy of the CBOE Put Protection Index (PPUT) makes profit; particularly during which market conditions. Given the description ...
3
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1answer
460 views

What is The Closed-Form Implied Volatility Estimator (As Defined by Hallerbach 2004) for A Put Option?

"An Improved Estimator For Black-Scholes-Merton Implied Volatility" by Hallerbach (2004) (link to article) provides an equation (Eq. 24, Page 13, and below) for the implied volatility of a call option....
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1answer
1k views

Put call parity in practice

I understand the Wikipedia article for put-call parity on a theoretical level: if you magically had portfolios consisting of 1) long a call, short a put, and 2) long the stock, short a discounted ...
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0answers
77 views

Cox-Ross-Rubinstein - getting volatility

i have exam coming on financial engineering, and need help asap with this thing. Basically there's a European put option ex dividend. We know that the stock price is $S_t = 85$, the exercise price is $...
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1answer
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 ...
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1answer
314 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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1answer
1k views

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 ...
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3answers
409 views

A paradox about the American Put option price

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 ...
2
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1answer
820 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 ...
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2answers
132 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 ...
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1answer
135 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 ...
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1answer
4k 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 ...
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0answers
60 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 ...
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1answer
302 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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0answers
157 views

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 ...
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1answer
115 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?
2
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1answer
323 views

How to hedge a put under the Black-Scholes model?

To hedge a call, one would invest the option price proceeds into $\Delta_t*S_t + B_t = c_t$. (ok) However, a put has negative delta, so I would short $\Delta_t*S_t$ and invest $p_t+\Delta_t*S_t>...
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4answers
271 views

How to short an option?

It appears to me that retail investors can only buy calls and puts, but not short them through any standardized way (except maybe borrowing the option from a friend ;) ). Is that correct, or how can ...