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Bond equivalent yield =2[(1+r/4)^2-1]=8.08% Let n be the number of months in a period than rate per month=r/12*n Compounding the rate over 6 months 6/n times, Bond equivalent yield =2[(1+nr/12)^(6/n)-1] is the general formula where n:number of months in the period mentioned e.g. for semiannual...

dd1/dσ=d/dσ[ln(S/X)+T(r+.5σ^2)/σ*root(T)] dd1/dσ=[ σ*σT-(ln(S/X)+T(r+.5σ^2))/σ^2*root(T)] dd1/dσ=[-(ln(S/X)+T(r-.5σ^2))/σ^2*root(T)] dd1/dσ=[-d2/σ] dc/dσ= exp(-qT) [S N’(d1)* √T]=vega d(vega)/dσ= exp(-qT)S*√T*d/dσ(exp(-.5d1^2)) d(vega)/dσ=exp(-qT)S*√T*d/dd1(exp(-.5d1^2))dd1/dσ...

Caramel we can always find the derivatives of above greeks and equalise them to zero to get extrema. However its also possible to find derivatives of greeks with some other variable .I would illustrate this with following example. thanks

Valuation of interest rate Swap(using Forwards rate agreements): The fixed and floating rate payments in the future can be considered as a series of forward rate agreements FRA's which whereby two parties agree to exchange fixed rate for floating rate payment on a certain principal at...

Valuation of interest rate Swap: Pay 6 month libor and recieve fixed rate of 8% per annum. Suppose the swap life is 1.25 yrs or 15 months. The libor today is 10.2%. The payment is equivalent to floating rate bond which pays floating rate every 6 months and receipt is equivalent to a fixed rate...

Lets start discussion on comparative advantage: Suppose two parties A and B with following rates available to them: Fixed Floating A: 4% 6-month LIBOR-.1% B: 5.2% 6-month LIBOR+.6% Now A wants to borrow floating and B wants to borrow fixed. Than A and B can enter a swap agreement wherein A pays...

Swaps are used primarily for below purposes: 1. Convert a fixed rate liability to a floating rate liability. 2. Convert a floating rate liability to a fixed rate liability. 3. Convert a fixed rate investment to a floating rate investment . 4. Convert a floating rate investment to a fixed rate...

Thread on swaps: A swap is an agreement to exchange cash flows at certain specified future times according to certain specified rules. example An agreement by X to pay fixed rate of interest of 5% per annum for 6 months for a 6 month libor for 2 years on a notional principal of 100 million...

Garp it seems is not particularly concerned with such type of errors.there seems to be less scrutiny in such matters where Garp need to be more vigilant and meticulous. As Caramel pointed out errors in their practice exams which is really disappointing. Garp should revise and carefully...

Hi Caramel, yeah that is definitely possible that we find points of extrema for gamma,theta etc. But i think its already very long exercise but we can always find it. yeah if you insist i can do it for you.But these are the basic greek formulas that i derived from Black Scholes model with few...

This completes greeks theory from my side. any queries on how above results came and any mistake are wellcomed.... thanks

Applying put call parity to call we calculate the put prices: p+Sexp(-qT)=c+X*exp(-rT).......PCP 1) delta of put: differentiating both sides of PCP w.r.t S, dp/dS+ exp(-qT)=dc/dS dp/dS=dc/dS- exp(-qT)=delta of call- exp(-qT) dp/dS=exp(-qT) *N(d1)- exp(-qT) dp/dS=exp(-qT) *[N(d1)- 1]...

Lets discuss rho, Rho is the rate of change of value of a derivative w.r.t the interest rate Derivation of rho, c=Sexp(-q(T-t)*N(d1)-X* exp(-r(T-t))*N(d2) dc/dr=d/dr[Sexp(-q(T-t)*N(d1)-X* exp(-r(T-t))*N(d2)] dc/dr=d/dr[Sexp(-q(T-t)*N(d1)]-d/dr[X* exp(-r(T-t))*N(d2)]...

Lets discuss rho, Rho is the rate of change of value of a derivative w.r.t the interest rate Derivation of rho, c=Sexp(-q(T-t)*N(d1)-X* exp(-r(T-t))*N(d2) dc/dr=d/dr[Sexp(-q(T-t)*N(d1)-X* exp(-r(T-t))*N(d2)] dc/dr=d/dr[Sexp(-q(T-t)*N(d1)]-d/dr[X* exp(-r(T-t))*N(d2)]...

As far as I can understand that undiversified VaR tell you about how bad things can go. That is during downtime all the positions are affected in the same way that is the correlation between them increases so that they almost move in same direction. The maximum loss that can occur is...

David can expalin later but i think you might give a thought about my explaination also, undiversified VaR occurs when portfolio is not diversified so that there are no benefits of diversification. When positions move in opposite directions then the overall risk of the portfolio reduces to any...

Derivation of theta: c=Sexp(-q(T-t)*N(d1)-X* exp(-r(T-t))*N(d2) c=T1-T2 dc/dt=d(T1)/dt-d(T2)/dt d(T1)/dt=d/dt(Sexp(-q(T-t)*N(d1)) d(T1)/dt=(qSexp(-q(T-t)*N(d1)+Sexp(-q(T-t)*dN(d1)/dt) d(T1)/dt=(qSexp(-q(T-t)*N(d1)+Sexp(-q(T-t)*dN(d1)/dd1*dd1/dt) d1=[ln(S/X)+(T-t)(r+.5σ²)]/σ√T-t dd1/dt=√T-t*...

Hi today is turn of vega, Vega is nothing but rate of change of derivatives portfolio w.r.t. volatility of the underlying asset. Vega tends to be greatest for the option that are close to the money. derivation of vega, c=Sexp(-qT)*N(d1)-X* exp(-rT)*N(d2) dc/dσ= d/dσ [Sexp(-qT)*N(d1)-X...

According to property of binomial distribution of EDF, the variance of EDF is given by EDF*(1-EDF) or volatility of EDF is sqrt(EDF*(1-EDF)) therefore,volatility of Loan A=sqrt(.015*(1-.015))=12.155% volatility of Loan B=sqrt(.035*(1-.035))=18.378% The above values in the exhibit are nowhere...

Those of you wondering where the delta came from in the above derivation, call price, c=Sexp(-qT)*N(d1)-X*exp(-rT)*N(d2) c=Sexp(-qT)*N(d1)-X* exp(-rT)*N(d2) dc/dS= d/dS[Sexp(-qT)*N(d1)-X exp(-rT)*N(d2)] dc/dS= d/dS[Sexp(-qT)N(d1)]- exp(-rT)*d/dS[XN(d2)] dc/dS= exp(-qT) [N(d1)+S dN(d1)/dS]-X...