fCash Valuation 1

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Last updated 2 years ago

fCash Valuation 1

Do you know what the most critical part behind the fixed-rate products offered by Notional Finance is? fCash! Correct

But how are they valued?

A 🧵 on how to value fCash as a Lender and as a Borrower

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fCash is a digital representation of a bond that has both, an asset component (a claim on funds in the future) and a liability component (an obligation to repay principal + interest). Keep reading to know how exactly these fCash are valued across time.

Ref 🧵 for a quick refresher on fCash.

[Link to the thread]

---

Assume you are a lender and you wish to deposit 1000 DAI to get 5% APY in a span of 1 year. So, you should get 1051.27 DAI at the end of the year without considering fees.

Notional uses this future value to value the fDAI.

1 +ve fDAI = 1000 / 1051.27 = 0.9512 DAI

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To lend, you deposit 1000 DAI in Notional and it would swap cDAI equivalent to 1000 DAI for +ve fCash at an exchange rate of 0.9512 DAI in the fDAI 1-Year liquidity pool.

After the trade, you would have 1051.27 +ve fDAI

Ref 🧵 for a quick refresher on fCash markets.

[Link to the thread]

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After a year, we make the reverse computation i.e. discounting the future value to the present to value fDAI. Assuming the rates are still 5% and the duration has reduced to "0" as the bond is about to mature (you held the funds for a full year). On discounting, the PV of your 1051.27 +ve fDAI is 1051.27 DAI.

Therefore 1 +ve fDAI = 1 DAI

---

Notional account would swap your 1051.27 +ve fDAI for 1051.27 DAI worth of cDAI.

You can convert your assets to 1051.27 DAI or can earn the compound variable rates on your cDAI tokens.

But what happens if you want to exit before 1 year (3 months for example)?

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Continuing our example where you had 1051.27 +ve fDAI, and you want to exit after 3 months.

To compute the value of your fDAI, let us assume the rates are still at 5% and the duration has reduced to "3/4". The Duration refers to the time left to maturity.

On discounting, the PV of your 1051.27 +ve fDAI is 1012.57 DAI.

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The exchange rate turns out to be 0.963 (1012.57 / 1051.27) and on exiting, the Notional account would swap your 1051.27 +ve fDAI for 1012.57 DAI worth of cDAI.

One of the core assumptions in all the examples in the thread is the consideration of fees to be zero.

That's a wrap

---

[OPTIONAL]

We are bringing a series of threads to better understand a large and complex codebase (~12,000+ lines of Solidity!) most simplistically.

👀 What's upcoming?

🔹 Fees at Notional for Lending & Borrowing trades

🔹 fCash valuation tool for Lenders

---

Appendix

$Future Value = PresentValue(e^{Rate*Duration})$

$1051.27 = 1000(e^{0.05*1})$

---

$PresentValue = FutureValue(e^{-Rate*Duration})$

$1051.27=1051.27(e^{-0.05*0})$

---

$LendDuration=0.25Year$

$Maturity = 1Year$

$TimeToMaturity=1-LendDuration=0.75$

$PresentValue = FutureValue(e^{-Rate*Duration})$

$1012.57=1051.27(e^{-0.05*0.75})$

---

$Future Value = PresentValue(e^{Rate*Duration})$

$1048.12 = 1000(e^{(0.05-0.003)*1})$

PreviousAMM Overview and Trades NextLiquidity Fees

Last updated 2 years ago

Do you know what the most critical part behind the fixed-rate products offered by Notional Finance is? fCash! Correct

But how are they valued?

A 🧵 on how to value fCash as a Lender and as a Borrower

---

Ref 🧵 for a quick refresher on fCash.

[Link to the thread]

---

Assume you are a lender and you wish to deposit 1000 DAI to get 5% APY in a span of 1 year. So, you should get 1051.27 DAI at the end of the year without considering fees.

Notional uses this future value to value the fDAI.

1 +ve fDAI = 1000 / 1051.27 = 0.9512 DAI

---

To lend, you deposit 1000 DAI in Notional and it would swap cDAI equivalent to 1000 DAI for +ve fCash at an exchange rate of 0.9512 DAI in the fDAI 1-Year liquidity pool.

After the trade, you would have 1051.27 +ve fDAI

Ref 🧵 for a quick refresher on fCash markets.

[Link to the thread]

---

Therefore 1 +ve fDAI = 1 DAI

---

Notional account would swap your 1051.27 +ve fDAI for 1051.27 DAI worth of cDAI.

You can convert your assets to 1051.27 DAI or can earn the compound variable rates on your cDAI tokens.

But what happens if you want to exit before 1 year (3 months for example)?

---

Continuing our example where you had 1051.27 +ve fDAI, and you want to exit after 3 months.

To compute the value of your fDAI, let us assume the rates are still at 5% and the duration has reduced to "3/4". The Duration refers to the time left to maturity.

On discounting, the PV of your 1051.27 +ve fDAI is 1012.57 DAI.

---

The exchange rate turns out to be 0.963 (1012.57 / 1051.27) and on exiting, the Notional account would swap your 1051.27 +ve fDAI for 1012.57 DAI worth of cDAI.

One of the core assumptions in all the examples in the thread is the consideration of fees to be zero.

That's a wrap

---

[OPTIONAL]

We are bringing a series of threads to better understand a large and complex codebase (~12,000+ lines of Solidity!) most simplistically.

👀 What's upcoming?

🔹 Fees at Notional for Lending & Borrowing trades

🔹 fCash valuation tool for Lenders

---

Appendix

$Future Value = PresentValue(e^{Rate*Duration})$

$1051.27 = 1000(e^{0.05*1})$

---

$PresentValue = FutureValue(e^{-Rate*Duration})$

$1051.27=1051.27(e^{-0.05*0})$

---

$LendDuration=0.25Year$

$Maturity = 1Year$

$TimeToMaturity=1-LendDuration=0.75$

$PresentValue = FutureValue(e^{-Rate*Duration})$

$1012.57=1051.27(e^{-0.05*0.75})$

---

Appendix

FutureValue=PresentValue(eRate∗Duration)Future Value = PresentValue(e^{Rate*Duration})FutureValue=PresentValue(eRate∗Duration)

1051.27=1000(e0.05∗1)1051.27 = 1000(e^{0.05*1})1051.27=1000(e0.05∗1)

PresentValue=FutureValue(e−Rate∗Duration)PresentValue = FutureValue(e^{-Rate*Duration})PresentValue=FutureValue(e−Rate∗Duration)

1051.27=1051.27(e−0.05∗0)1051.27=1051.27(e^{-0.05*0})1051.27=1051.27(e−0.05∗0)

LendDuration=0.25YearLendDuration=0.25YearLendDuration=0.25Year

Maturity=1YearMaturity = 1YearMaturity=1Year

TimeToMaturity=1−LendDuration=0.75TimeToMaturity=1-LendDuration=0.75TimeToMaturity=1−LendDuration=0.75

PresentValue=FutureValue(e−Rate∗Duration)PresentValue = FutureValue(e^{-Rate*Duration})PresentValue=FutureValue(e−Rate∗Duration)

1012.57=1051.27(e−0.05∗0.75)1012.57=1051.27(e^{-0.05*0.75})1012.57=1051.27(e−0.05∗0.75)

FutureValue=PresentValue(eRate∗Duration)Future Value = PresentValue(e^{Rate*Duration})FutureValue=PresentValue(eRate∗Duration)

1048.12=1000(e(0.05−0.003)∗1)1048.12 = 1000(e^{(0.05-0.003)*1})1048.12=1000(e(0.05−0.003)∗1)

Appendix

FutureValue=PresentValue(eRate∗Duration)Future Value = PresentValue(e^{Rate*Duration})FutureValue=PresentValue(eRate∗Duration)

1051.27=1000(e0.05∗1)1051.27 = 1000(e^{0.05*1})1051.27=1000(e0.05∗1)

PresentValue=FutureValue(e−Rate∗Duration)PresentValue = FutureValue(e^{-Rate*Duration})PresentValue=FutureValue(e−Rate∗Duration)

1051.27=1051.27(e−0.05∗0)1051.27=1051.27(e^{-0.05*0})1051.27=1051.27(e−0.05∗0)

LendDuration=0.25YearLendDuration=0.25YearLendDuration=0.25Year

Maturity=1YearMaturity = 1YearMaturity=1Year

TimeToMaturity=1−LendDuration=0.75TimeToMaturity=1-LendDuration=0.75TimeToMaturity=1−LendDuration=0.75

PresentValue=FutureValue(e−Rate∗Duration)PresentValue = FutureValue(e^{-Rate*Duration})PresentValue=FutureValue(e−Rate∗Duration)

1012.57=1051.27(e−0.05∗0.75)1012.57=1051.27(e^{-0.05*0.75})1012.57=1051.27(e−0.05∗0.75)

FutureValue=PresentValue(eRate∗Duration)Future Value = PresentValue(e^{Rate*Duration})FutureValue=PresentValue(eRate∗Duration)

1048.12=1000(e(0.05−0.003)∗1)1048.12 = 1000(e^{(0.05-0.003)*1})1048.12=1000(e(0.05−0.003)∗1)

$Future Value = PresentValue(e^{Rate*Duration})$

$1051.27 = 1000(e^{0.05*1})$

$PresentValue = FutureValue(e^{-Rate*Duration})$

$1051.27=1051.27(e^{-0.05*0})$

$LendDuration=0.25Year$

$Maturity = 1Year$

$TimeToMaturity=1-LendDuration=0.75$

$PresentValue = FutureValue(e^{-Rate*Duration})$

$1012.57=1051.27(e^{-0.05*0.75})$

$Future Value = PresentValue(e^{Rate*Duration})$

$1048.12 = 1000(e^{(0.05-0.003)*1})$

$Future Value = PresentValue(e^{Rate*Duration})$

$1051.27 = 1000(e^{0.05*1})$

$PresentValue = FutureValue(e^{-Rate*Duration})$

$1051.27=1051.27(e^{-0.05*0})$

$LendDuration=0.25Year$

$Maturity = 1Year$

$TimeToMaturity=1-LendDuration=0.75$

$PresentValue = FutureValue(e^{-Rate*Duration})$

$1012.57=1051.27(e^{-0.05*0.75})$

$Future Value = PresentValue(e^{Rate*Duration})$

$1048.12 = 1000(e^{(0.05-0.003)*1})$