scholarly journals Explicit Pricing Formulas for European Option with Asset Exposed to Double Defaults Risk

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Taoshun He
Keyword(s):  
Default Risk ◽  
Asset Price ◽  
European Option ◽  
Put Options ◽  
Default Time ◽  
Novel Technique ◽  
Endogenous Default ◽  
Option Model ◽  
Analytical Formulas

We derive analytical formulas for European call and put options on underlying assets that are exposed to double defaults risks which include exogenous counterparty default risk and endogenous default risk. The endogenous default risk leads the asset price to drop to zero and the exogenous counterparty default risk induces a drop in the asset price, but the asset can still be traded after this default time. A novel technique is developed to evaluate the European call and put options by first conditioning on the predefault and the postdefault time and then obtaining the unconditional analytic formulas for their price. We also compare the pricing results of our model with default-free option model and counterparty default risk option model.

scholarly journals Option Pricing for Path-Dependent Options with Assets Exposed to Multiple Defaults Risk

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Taoshun He
Keyword(s):  
Option Pricing ◽  
Default Risk ◽  
Asset Price ◽  
Default Time ◽  
Original Technique ◽  
Endogenous Default ◽  
Lookback Options ◽  
Option Model ◽  
Analytical Formulas ◽  
Path Dependent

In the present paper, we derive analytical formulas for barrier and lookback options with underlying assets exposed to multiple defaults risks which include exogenous counterparty default risk and endogenous default risk. The endogenous default risk leads the asset price drop to zero and the exogenous counterparty default risk induces a drop in the asset price, but the asset can still be traded after this default time. An original technique is developed to valuate the barrier and lookback options by first conditioning on the predefault and the afterdefault time and then obtaining the unconditional analytic formulas for their price. We also compare the pricing results of our model with the default-free option model and exogenous counterparty default risk option model.

scholarly journals Pricing Formula for Exotic Options with Assets Exposed to Counterparty Risk

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Li Yan
Keyword(s):  
Asset Price ◽  
Exotic Options ◽  
Barrier Options ◽  
Counterparty Risk ◽  
Default Time ◽  
Novel Technique ◽  
Analytical Formulas ◽  
Pricing Formula

This paper gives analytical formulas for lookback and barrier options on underlying assets that are exposed to a counterparty risk. The counterparty risk induces a drop in the asset price, but the asset can still be traded after this default time. A novel technique is developed to valuate the lookback and barrier options by first conditioning on the predefault and the postdefault time and then obtain the unconditional analytic formulas for their prices.

scholarly journals Pricing Perpetual American Put Options with Asset-Dependent Discounting

2021 ◽  
Vol 14 (3) ◽  
pp. 130
Author(s):  
Jonas Al-Hadad ◽  
Zbigniew Palmowski
Keyword(s):  
Value Function ◽  
Asset Price ◽  
Stopping Times ◽  
Martingale Measure ◽  
Put Options ◽  
American Put Options ◽  
Exact Calculations ◽  
Negative Exponential ◽  
American Put ◽  
The Value Function

The main objective of this paper is to present an algorithm of pricing perpetual American put options with asset-dependent discounting. The value function of such an instrument can be described as VAPutω(s)=supτ∈TEs[e−∫0τω(Sw)dw(K−Sτ)+], where T is a family of stopping times, ω is a discount function and E is an expectation taken with respect to a martingale measure. Moreover, we assume that the asset price process St is a geometric Lévy process with negative exponential jumps, i.e., St=seζt+σBt−∑i=1NtYi. The asset-dependent discounting is reflected in the ω function, so this approach is a generalisation of the classic case when ω is constant. It turns out that under certain conditions on the ω function, the value function VAPutω(s) is convex and can be represented in a closed form. We provide an option pricing algorithm in this scenario and we present exact calculations for the particular choices of ω such that VAPutω(s) takes a simplified form.

scholarly journals Series representation of the pricing formula for the European option driven by space-time fractional diffusion

2018 ◽  
Vol 21 (4) ◽  
pp. 981-1004 ◽  
Author(s):  
Jean-Philippe Aguilar ◽  
Cyril Coste ◽  
Jan Korbel
Keyword(s):  
Asset Price ◽  
Series Representation ◽  
Option Price ◽  
Double Series ◽  
Fractional Diffusion ◽  
Space Time ◽  
Esscher Transform ◽  
European Option ◽  
Underlying Asset ◽  
European Call Option

Abstract In this paper, we show that the price of an European call option, whose underlying asset price is driven by the space-time fractional diffusion, can be expressed in terms of rapidly convergent double-series. This series formula is obtained from the Mellin-Barnes representation of the option price with help of residue summation in ℂ2. We also derive the series representation for the associated risk-neutral factors, obtained by Esscher transform of the space-time fractional Green functions.

An Empirical Study on Implied Volatility Skew Using PCA

2016 ◽  
Vol 24 (3) ◽  
pp. 365-397
Author(s):  
Jin Woo Kim ◽  
Joon H. Rhee
Keyword(s):  
Financial Crisis ◽  
Implied Volatility ◽  
Structural Changes ◽  
Explanatory Power ◽  
Asset Price ◽  
Option Price ◽  
Principal Component ◽  
Underlying Asset ◽  
Put Options ◽  
Two Factors

This paper extracts the factors determining the implied volatility skew movements of KOSPI200 index options by applying PCA (Principal Component Analysis). In particular, we analyze the movement of skew depending on the changes of the underlying asset price. As a result, it turned out that two factors can explain 94.6%~99.8% of the whole movement of implied volatility. The factor1 could be interpreted as ‘parallel shift’, and factor2 as the movement of ‘tilt or slope’. We also find some significant structural changes in the movement of skew after the Financial Crisis. The explanatory power of factor1 becomes more important on the movement of skew in both call and put options after the financial crisis. On the other hand, the influences of the factor2 is less. In general, after financial crisis, the volatility skew has the strong tendency to move in parallel. This implies that the changes in the option price or implied volatility due to the some shocks becomes more independent of the strike prices.

Binomial tree method for option pricing: Discrete Carr and Madan formula approach

2021 ◽  
pp. 2150024
Author(s):  
Yoshifumi Muroi ◽  
Ryota Saeki ◽  
Shintaro Suda
Keyword(s):  
Option Pricing ◽  
Broad Class ◽  
Asset Price ◽  
Option Prices ◽  
European Option ◽  
Tree Model ◽  
Binomial Tree ◽  
Tree Models ◽  
Binomial Tree Model ◽  
Tree Method

This paper suggests a new Fourier analysis approach to evaluate the option prices and its sensitivities (Greeks) using the binomial tree model. In the last half of this paper, we show that option prices are efficiently and effectively evaluated using a semi-closed form formula for European option prices. We can compute option prices in a broad class of jump-diffusion models because we calculate the characteristic function for an underlying asset price numerically. Furthermore, we also compute the price of European options in the exp-Levy model. This numerical experiment gives new insights into option pricing in the nonparametric Levy model. The option prices and sensitivities can be computed very accurately and efficiently, even in binomial tree models with jumps.

Reflected and doubly reflected BSDEs driven by RCLL martingales

2021 ◽  
Author(s):  
Tianyang Nie ◽  
Marek Rutkowski
Keyword(s):  
Brownian Motion ◽  
Default Risk ◽  
Financial Models ◽  
Wide Spectrum ◽  
Random Measure ◽  
One Dimensional ◽  
Default Time ◽  
Working Paper ◽  
And Control ◽  
Reflected Bsdes

We prove some new results on reflected BSDEs and doubly reflected BSDEs driven by a multi-dimensional RCLL martingale. The goal is to develop a general multi-asset framework encompassing a wide spectrum of nonlinear financial models, including as particular cases the setups studied by Peng and Xu [BSDEs with random default time and their applications to default risk, working paper, preprint (2009), arXiv:0910.2091] and Dumitrescu et al. [BSDEs with default jump, in Computation and Combinatorics in Dynamics, Stochastics and Control, Abel Symposia, Vol. 13, eds. E. Celledoni, G. Di Nunno, K. Ebrahimi-Fard and H. Munthe-Kaas (Springer, Cham, 2018), pp. 233–263] who examined BSDEs driven by a one-dimensional Brownian motion and a purely discontinuous martingale with a single jump. Our results are not covered by existing literature on reflected and doubly reflected BSDEs driven by a Brownian motion and a Poisson random measure.

Optimal bank interest margin under capital regulation: bank as a liquidity provider

2019 ◽  
Vol 11 (2) ◽  
pp. 158-173 ◽  
Author(s):  
Fu-Wei Huang ◽  
Shi Chen ◽  
Jeng-Yan Tsai
Keyword(s):  
Default Risk ◽  
Banking System ◽  
Capital Regulation ◽  
Knock Out ◽  
Content Type ◽  
Loan Rate ◽  
Negative Effect ◽  
Demand Deposits ◽  
Option Model ◽  
Interest Margin

Purpose This paper aims to develop a barrier cap option model, i.e. a cap option model where default can occur at any time before the maturity date, to evaluate the equity and the default risk of a bank. The model implies the bank as a liquidity provider that one institution carriers out both lending and deposit-taking functions under the same roof. This paper studies the impacts of demand deposits and capital regulation on the optimal bank interest margin, i.e. the spread between the loan rate and the deposit rate. Design/methodology/approach This paper characterizes the bank’s equity value by a barrier cap option framework. In the model, default can occur at any time before the maturity and loan markets are imperfectly competitive. Findings This paper has two main results. First, increases in demand deposits reduce the bank’s interest margin and further increase the bank’s default risk. The negative effect on the optimal bank interest margin which ignores the barrier leads to significant overestimation; the positive effect on the default risk which ignores the barrier leads to underestimation. Second, the same pattern of capital regulation as previously applies. Capital regulation as such makes the bank more prone to loan risk-taking, thereby adversely affecting the stability of banking system. Originality/value This paper reintroduces the knock-out value and bank interest margin determination within a synergy banking function to the cap option model. The results confirm the need to model bank equity as a barrier cap option and demonstrate its usefulness in capital regulation.

scholarly journals Fund Managers, Career Concerns, and Asset Price Volatility

2012 ◽  
Vol 102 (5) ◽  
pp. 1986-2017 ◽  
Author(s):  
Veronica Guerrieri ◽  
Péter Kondor
Keyword(s):  
Portfolio Management ◽  
Default Risk ◽  
Asset Price ◽  
Price Volatility ◽  
Career Concerns ◽  
Past Performance ◽  
Fund Managers ◽  
Risky Bonds ◽  
Delegated Portfolio Management ◽  
Changes Over Time

We propose a model of delegated portfolio management with career concerns. Investors hire fund managers to invest their capital either in risky bonds or in riskless assets. Some managers have superior information on default risk. Based on past performance, investors update beliefs on managers and make firing decisions. This leads to career concerns that affect managers' investment decisions, generating a countercyclical “reputational premium.” When default risk is high, return on bonds is high to compensate uninformed managers for the high risk of being fired. As default risk changes over time, the reputational premium amplifies price volatility. (JEL G11, G12, G23, L84)

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